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×#13285 |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 3 generators on 191 points:
(1,2)(3,7)(4,5)(6,8)(9,10,15,20,16,21,14,31)(11,22,26,38,27,39,25,34)(12,19,13,30,29,33,28,18)(17,32,35,40,36,23,37,24)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191);(2,5)(6,7)(9,11,13,24,15,26,29,32,16,27,28,40,14,25,12,23)(10,17,33,39,31,37,30,38,21,36,19,22,20,35,18,34);(1,3,4,8)(2,6,5,7)(9,12,14,28,16,29,15,13)(10,18,20,19,21,30,31,33)(11,23,25,40,27,32,26,24)(17,34,35,22,36,38,37,39)11476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6273);