Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C2×C4 |
| direct product | C151×#11715 |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 175 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 175 points:
(2,5,6,7)(9,10)(11,15)(12,19,20,14)(13,16)(17,23,24,21)(18,22)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175);(1,2)(3,7)(4,6)(5,8)(10,14,16,19)(12,20)(15,21,22,23)(17,24);(9,11,13,18)(10,15,16,22)(12,17,20,24)(14,21,19,23)6946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 4703);