Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#19003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C151 |
| prime radical | #532×C151 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 4 generators on 199 points:
(3,9)(4,11)(6,14)(7,12)(10,13)(15,16)(17,18)(19,29)(20,33)(21,28)(22,27)(23,26)(24,31)(25,34)(30,38)(32,41)(35,42)(36,39)(37,40)(43,45)(44,47)(46,48)(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);(1,2,5,8)(3,6,10,15)(4,12,11,7)(9,16,13,14)(17,19)(18,24)(20,30)(21,36)(22,31)(23,32)(25,38)(26,39)(27,41)(28,29)(33,47)(34,45)(35,46)(37,44)(40,48)(42,43);(1,3)(2,6)(4,13)(5,10)(7,16)(8,15)(9,11)(12,14)(17,20,23,35)(18,25,26,40)(19,30,32,46)(21,34,22,37)(24,38,39,48)(27,33,28,42)(29,43,41,47)(31,44,36,45);(18,26)(24,39)(25,40)(27,28)(29,41)(33,42)(38,48)(43,47)5134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 11991);