"Source: Text/Group/GrpASim.text";
"Line: 1622";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpASim.text, line: 1622
// Example: H72E6 ()
print "Example: H72E6";
ei := GetEchoInput();
SetEchoInput(true);
SetSeed(1);
G := Omega(7, 5);
flag, name := SimpleGroupName(G);
name;
F := GF(3);
P := GL(5,F);
gens := [
P![2,1,2,1,2,2,0,0,0,2,0,2,0,0,0,0,1,2,0,1,1,0,2,2,1],
P![2,1,0,2,1,1,2,0,2,2,1,1,2,1,1,0,2,0,1,1,1,1,2,2,2]];
G := sub <P | gens>;
flag, name := SimpleGroupName(G);
flag;
assert $1;
name;
/* naming an alternating group */
G := MatrixGroup<4, GF(2) |
   [ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0 ],
   [ 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0 ] >;
flag, name := SimpleGroupName(G);
flag;
assert $1;
/* this is A5 */
name; 
/* naming a classical group */
F := GF(7^2);
P := GL (6,F);
w := PrimitiveElement (F);
gens := [
P![w^12,w^36,  0,  5,  2,  0,w^44,w^36,  0,  6,  2,  0,
w^42,w^42,w^28,w^22,w^22,  3,  4,  3,  0,w^36,w^12,  0,
2,  3,  0,w^20,w^12,  0,w^14,w^14,  1,w^18,w^18, w^4],
P![w^38,w^26,w^25,w^21, w^9,  3,w^21,w^45,w^33, w^4,w^28,
2,  6,  4, w^1, w^7,w^15,  4,  1,w^36,w^35, w^5,w^41,  5,
w^31, w^7,w^43,w^36,w^12,  1,w^34,w^42,w^11,w^39,w^47,  2]
];
G := sub <P | gens>;
flag, name := LieType(G, 5);
flag;
assert $1;
name;
/* so this is SL(2, 5) */ 
SetEchoInput(ei);
