Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C113 · Schur multiplier (H2) = C22 |
| direct product | C113×#11721 |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 3 generators on 137 points:
(2,5,6,7)(9,10,13,18,14,17,19,22)(11,15,21,23,20,24,12,16)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,2)(3,7)(4,6)(5,8)(9,11)(10,15,17,24)(12,19)(13,21)(14,20)(16,22,23,18);(9,12,14,21)(10,16,17,23)(11,19,20,13)(15,22,24,18)5198 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 4709);