From 12d0bd897f100a4d2d60061323cf9fe7005ad037 Mon Sep 17 00:00:00 2001
From: kalmarek <kalmar@amu.edu.pl>
Date: Thu, 23 Apr 2020 16:45:32 +0200
Subject: [PATCH] add two 555 examples

---
 Makefile                     | 3 +--
 data/presentations_5_5_5.txt | 8 ++++++++
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/Makefile b/Makefile
index 6f24293..810e345 100644
--- a/Makefile
+++ b/Makefile
@@ -8,8 +8,7 @@ GROUPS344 = 14_40_40_0 14_40_48_0 14_40_54_0 14_40_54_2 14_48_48_0 14_48_48_1 14
 
 GROUPS444 = 40_40_40_0 40_40_48_0 40_40_54_0 40_48_48_0 40_48_54_0 40_48_54_2 40_54_54_0 40_54_54_2 40_54_54_8 48_48_48_0 48_48_48_1 48_48_54_0 48_54_54_0 48_54_54_2 48_54_54_8 54_54_54_0 54_54_54_2
 
-GROUPS555 = H_1 H_2 H_3 H_4 H_5 H_6 H_7 H_8
-
+GROUPS555 = H_1 H_2 H_3 H_4 H_5 H_6 H_7 H_8 Hyp1 Hyp2
 
 JULIA = /opt/bin/julia
 
diff --git a/data/presentations_5_5_5.txt b/data/presentations_5_5_5.txt
index c0927b3..f5fada2 100644
--- a/data/presentations_5_5_5.txt
+++ b/data/presentations_5_5_5.txt
@@ -20,3 +20,11 @@ H_6:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a
 H_7:=Group<a, b, c |a^5, b^5, c^5, comm(a, b, a), comm(a, b, b), b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, comm(a,c,a), comm(a,c,c,a), comm(a,c,c,c)>;
 //H_8
 H_8:=Group<a, b, c |a^5, b^5, c^5, a^-1 * b * a * b^-1 * a * b, b^-2 * a * b * a * b^-2 * a^2, b^-1 * c * b * c^-1 * b * c, c^-2 * b * c * b * c^-2 * b^2, comm(a,c,a), comm(a,c,c,a), comm(a,c,c,c)>;
+//
+// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ Heisenberg(F₅)
+//
+Hyp1:=Group<a, b, c | a^5, b^5, c^5, comm(a, c), b^-1 * c^-1 * b * c * b * c^-1 * b^-1 * c, b * c^-2 * b * c * b^-2 * c, a * b * a * b^-1 * a^-1 * b * a * b * a^-1 * b^-1 * a^-1 * b * a * b^-1* a^-1 * b^-1, b * a * b * a * b^2 * a^-1 * b * a^2 * b^-2 * a^-1 * b * a^-1 * b^-1 * a^2, b * a^-1 * b * a * b^-1 * a * b^2 * a^-1 * b * a * b^-1 * a * b * a^-1 * b^-1 * a^2, b * a * b^-1 * a * b * a^-1 * b * a^-2 * b^-1 * a^-1 * b * a^-1 * b^-1 * a * b^-1 * a^2, b * a^-1 * b * a^-1 * b^-2 * a * b^-1 * a^-1 * b^-1 * a^-1 * b * a^-2 * b^-2 * a^2, a * b * a^-2 * b^-1 * a^-1 * b^-1 * a^-1 * b^-2 * a * b^-1 * a^-2 * b^2 * a * b^-1, b * a^-2 * b^-1 * a^-2 * b * a * b^-1 * a * b^-1 * a^2 * b^-1 * a * b * a^-2 * b>;
+//
+// Group with <a, b> ≅ PSL₂(109), <b, c> ≅ SL₂(5)
+//
+Hyp2:=Group<a, b, c | a^5, b^5, c^5, comm(a, c), b * c^-1 * b * c * b^-1 * c, b^2 * c^-1 * b^-1 * c^-1 * b^2 * c^-2, a * b * a * b^-1 * a^-1 * b * a * b * a^-1 * b^-1 * a^-1 * b * a * b^-1 * a^-1 * b^-1, b * a * b * a * b^2 * a^-1 * b * a^2 * b^-2 * a^-1 * b * a^-1 * b^-1 * a^2, b * a^-1 * b * a * b^-1 * a * b^2 * a^-1 * b * a * b^-1 * a * b * a^-1 * b^-1 * a^2, b * a * b^-1 * a * b * a^-1 * b * a^-2 * b^-1 * a^-1 * b * a^-1 * b^-1 * a * b^-1 * a^2, b * a^-1 * b * a^-1 * b^-2 * a * b^-1 * a^-1 * b^-1 * a^-1 * b * a^-2 * b^-2 * a^2, a * b * a^-2 * b^-1 * a^-1 * b^-1 * a^-1 * b^-2 * a * b^-1 * a^-2 * b^2 * a * b^-1, b * a^-2 * b^-1 * a^-2 * b * a * b^-1 * a * b^-1 * a^2 * b^-1 * a * b * a^-2 * b>;