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add magma representations && parsing

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kalmarek 2019-12-18 00:33:01 +01:00
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// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;

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// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;

27
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// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;
// 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>;

51
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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)
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})
rels_expr = Meta.parse.(rels_str)
expr = :([$(rels_expr...)])
F = FreeGroup(String.(gens_str))
relations = @eval begin
a,b,c = AbstractAlgebra.gens($F)
$expr
end
return F/relations
end
function parse_grouppresentations(filename::AbstractString)
groups_strs = readlines(filename)
groups = Dict{String, FPGroup}()
names_idcs = findall(x->startswith(x, "//"), groups_strs)
push!(names_idcs, names_idcs[end]+1)
for (first_idx, next_idx) in zip(names_idcs, Iterators.rest(names_idcs, 2))
m = match(r"//\s?((\d{2}\s){2}\d\d).*", groups_strs[first_idx])
name = replace(m.captures[1], " "=>"_")
for idx in first_idx+1:next_idx-1
m = match(r"(.*)\s:=\sGroup<(.*)\|(.*)>", groups_strs[idx])
if isnothing(m)
@warn "Can't parse presentation at line $idx:\n $(str[idx])"
else
group_name = "$(name)_$(m.captures[1])"
G = parse_magma_grouppresentation(m.captures[2], m.captures[3])
groups[group_name] = G
end
end
end
return groups
end