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move to the saner group parsing

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kalmarek 2020-02-12 01:10:52 +01:00
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commit 2a7d121e13
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4 changed files with 199 additions and 178 deletions
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data/presentations_3_3_4.txt
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@ -1,123 +1,123 @@
// 14 14 40 0 4
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_14_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
G_14_14_40_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 14 48 0 1 4 5
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_5 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_14_14_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_14_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
G_14_14_48_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_14_48_5 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 14 14 54 0 4
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_14_14_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_14_54_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c^-1 * b * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 14 16 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_16_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 16 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_14_16_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_16_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 14 16 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_16_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_16_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 14 18 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_18_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 18 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_14_18_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 14 18 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_18_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_18_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 14 24 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_24_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 24 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_14_24_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_24_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 14 24 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_24_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_24_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 14 26 40 0 4
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_26_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
G_14_26_40_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 26 48 0 1 4 5
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_5 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_14_26_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_26_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
G_14_26_48_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_26_48_5 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 14 26 54 0 2 4 6
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_6 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_26_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_26_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_14_26_54_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_26_54_6 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 16 16 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_16_16_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 16 16 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_16_16_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_16_16_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 16 16 54 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_16_16_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 16 18 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_16_18_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 16 18 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_16_18_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 16 18 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_16_18_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_18_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 16 24 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_16_24_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 16 24 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_16_24_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_16_24_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 16 24 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_16_24_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_24_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 16 26 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_16_26_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 16 26 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_16_26_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_16_26_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 16 26 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_16_26_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_26_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 18 18 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_18_18_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 18 18 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_18_18_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 18 18 54 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_18_18_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b^-1 * c * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 18 24 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_18_24_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 18 24 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_18_24_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 18 24 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_18_24_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_18_24_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 18 26 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_18_26_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 18 26 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_18_26_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 18 26 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_18_26_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_18_26_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 24 24 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_24_24_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 24 24 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_24_24_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_24_24_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 24 24 54 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_24_24_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 24 26 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_24_26_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 24 26 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_24_26_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_24_26_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 24 26 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_24_26_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_24_26_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 26 26 40 0 4
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_26_26_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
G_26_26_40_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 26 26 48 0 1 4 5
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_5 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_26_26_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_26_26_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
G_26_26_48_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_26_26_48_5 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 26 26 54 0 4
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_4 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_26_26_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c * b, c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_26_26_54_4 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b^-1 * c * b^-1, c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >

108
data/presentations_3_4_4.txt
View File

@ -1,84 +1,84 @@
// 14 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_14_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 14 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_14_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 14 40 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_40_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 14 48 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_14_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_14_48_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 14 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_14_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 14 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_14_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_14_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_14_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b * a, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 16 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_16_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 16 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_16_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 16 40 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_16_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_40_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 16 48 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_16_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_16_48_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 16 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_16_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 16 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_16_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_16_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_16_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a^-1 * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 18 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_18_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 18 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_18_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 18 40 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_18_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_18_40_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 18 48 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_18_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 18 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_18_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_18_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 18 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_18_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_18_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_18_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a^-1 * b * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 24 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_24_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 24 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_24_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 24 40 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_24_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_24_40_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 24 48 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_24_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_24_48_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 24 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_24_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_24_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 24 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_24_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_24_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_24_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 26 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_26_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 26 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_26_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 26 40 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_26_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_26_40_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 26 48 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_26_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_26_48_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 26 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_26_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_26_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 26 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_26_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_26_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_26_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b * a, b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >

34
data/presentations_4_4_4.txt
View File

@ -1,27 +1,27 @@
// 40 40 40 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1>;
G_40_40_40_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c^-1 * a * c * a * c^-1 * a * c, a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1 >
// 40 40 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_40_40_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 40 40 54 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_40_40_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b^-1 * c * b * c * b^-1 * c * b, c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 40 48 48 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_40_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
// 40 48 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_40_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_40_48_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
// 40 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_40_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_40_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_40_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a^-1 * b * a * b * a^-1 * b * a, b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 48 48 48 0 1
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1>;
G_1 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c>;
G_48_48_48_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1 >
G_48_48_48_1 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c >
// 48 48 54 0
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_48_48_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 48 54 54 0 2 8
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_8 := Group<a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_48_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_48_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >
G_48_54_54_8 := Group< a, b, c | a^3, b^3, c^3, b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1, b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1, b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
// 54 54 54 0 2
G_0 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1, b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c>;
G_2 := Group<a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1, b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a>;
G_54_54_54_0 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1, b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1, a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c >
G_54_54_54_2 := Group< a, b, c | a^3, b^3, c^3, b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1, b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a, c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1, c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b, c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1, c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a >

75
src/groupparse.jl
View File

@ -1,17 +1,39 @@
function parse_magma_grouppresentation(str::AbstractString)
m = match(r".*Group<(.*)\|(.*)>", str)
gens_str = strip.(split(m.captures[1], ", "))
rels_str = strip.(split(m.captures[2], ", "))
return parse_magma_grouppresentation(gens_str, rels_str)
comm(a,b) = inv(a)*inv(b)*a*b
comm(a,b,args...) = comm(comm(a,b), args...)
const MAGMA_PRESENTATION_regex = r"Group<\s?(?<gens>.*)\s?\|\s?(?<rels>.*)\s?>"
const COMMUTATOR_regex = r"\((?<comm>[\w](\s?,\s?[\w]){1+})\)"
iscomment(line) = startswith(line, "//")
ismagma_presentation(line) = (m = match(MAGMA_PRESENTATION_regex, line); return !isnothing(m), m)
function parse_magma_fpgroup(str::AbstractString)
m = match(MAGMA_PRESENTATION_regex, str)
gens_str = strip.(split(m[:gens], ","))
rels_str = m[:rels]
split_indices = [0]
in_function_call=0
for (i,s) in enumerate(rels_str)
if s == '('
in_function_call += 1
elseif s == ')'
@assert in_function_call > 0
in_function_call -= 1
elseif s == ',' && iszero(in_function_call)
push!(split_indices, i)
end
end
@assert in_function_call == 0
push!(split_indices, length(rels_str)+1)
rels_strs = [strip.(String(rels_str[s+1:e-1])) for (s,e) in zip(split_indices, Iterators.rest(split_indices, 2))]
# rels_strs = replace.(rels_strs, COMMUTATOR_regex=> s"comm(\g<comm>)")
# @show rels_strs
return parse_magma_fpgroup(gens_str, rels_strs)
end
parse_magma_grouppresentation(gens_str::AbstractString, rels_str::AbstractString) =
parse_magma_grouppresentation(
strip.(split(gens_str, ", ")),
strip.(split(rels_str, ", "))
)
function parse_magma_grouppresentation(gens_str::AbstractVector{<:AbstractString}, rels_str::AbstractVector{<:AbstractString})
function parse_magma_fpgroup(gens_str::AbstractVector{<:AbstractString}, rels_str::AbstractVector{<:AbstractString})
rels_expr = Meta.parse.(rels_str)
expr = :([$(rels_expr...)])
@ -25,25 +47,24 @@ function parse_magma_grouppresentation(gens_str::AbstractVector{<:AbstractString
end
function parse_grouppresentations(filename::AbstractString)
groups_strs = readlines(filename)
lines = strip.(readlines(filename))
groups = Dict{String, FPGroup}()
names_idcs = findall(x->startswith(x, "//"), groups_strs)
push!(names_idcs, length(groups_strs)+1)
for (first_idx, next_idx) in zip(names_idcs, Iterators.rest(names_idcs, 2))
m = match(r"//\s?((\d{2}\s?){3}).*", groups_strs[first_idx])
name = replace(strip(m.captures[1]), " "=>"_")
for idx in first_idx+1:next_idx-1
m = match(r"G((_\d\d){3})?_(\d+)\s:=\sGroup<(.*)\|(.*)>", groups_strs[idx])
group_regex = r"(?<name>\w.*)\s?:=\s?(?<group_str>Group.*)"
for line in lines
isempty(line) && continue
iscomment(line) && continue
m = match(group_regex, line)
if isnothing(m)
@warn "Can't parse presentation at line $idx:\n $(groups_strs[idx])"
@warn "Can't parse presentation line\n $line"
continue
else
group_name = "$(name)_$(m.captures[3])"
G = parse_magma_grouppresentation(m.captures[4], m.captures[5])
groups[group_name] = G
name = strip(m[:name])
group_str = m[:group_str]
G = parse_magma_fpgroup(group_str)
if startswith(name, "G_")
name = name[3:end]
end
groups[name] = G
end
end
return groups