Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C24 |
| direct product | C151×#8503 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #379 |
| commutator | C42 | C22×C4×C151 |
| Frattini, cosocle | C2×C42 | C23×C151 |
| prime radical | #3554×C151 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 199 points:
(1,2,5,8,6,10,4,9)(3,11,12,7,13,15,14,16)(17,18)(19,27,30,23)(20,31,33,40)(21,26)(22,25)(24,32,38,34)(28,43)(29,42,47,37)(35,39)(36,44)(41,46)(45,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199);(1,3)(2,7)(4,14)(5,12)(6,13)(8,15)(9,11)(10,16)(17,19)(18,23)(20,28)(21,29)(22,30)(24,36)(25,27)(26,37)(31,48)(32,44)(33,45)(34,46)(35,47)(38,41)(39,42)(40,43);(2,8)(4,5)(7,15)(9,10)(11,16)(12,14)(17,20,22,33)(18,24,25,38)(19,28,30,45)(21,34,35,32)(23,36,27,41)(26,40,39,31)(29,46,47,44)(37,43,42,48)5134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 1491);