Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#9296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #386 |
| commutator | C42 | C22×C4×C151 |
| Frattini, cosocle | C2×C42 | C23×C151 |
| prime radical | C23×C151 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 191 points:
(1,2,4,6,5,8,3,7)(9,10,14,18,15,19,13,29)(11,20,24,31,23,35,22,16)(12,25,27,33,28,17,26,32)(21,34,38,30,37,40,36,39)(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);(2,6)(3,4)(7,8)(9,11)(10,16,19,31)(12,21)(13,22)(14,24)(15,23)(17,30,25,39)(18,20,29,35)(26,36)(27,38)(28,37)(32,40,33,34);(2,6)(3,4)(7,8)(9,12,15,28)(10,17,19,25)(11,21,23,37)(13,27,14,26)(16,30,31,39)(18,33,29,32)(20,34,35,40)(22,38,24,36)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 2284);