Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#23989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C151 |
| prime radical | #534×C151 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G | |
1210 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 191 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,15)(12,16)(13,17)(14,18)(19,29)(20,27)(21,28)(22,30)(23,31)(24,32)(25,33)(26,35)(34,39)(36,38)(37,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191);(1,3,4,8)(2,5,6,7)(9,11)(10,15)(12,19)(13,20)(14,21)(16,29)(17,27)(18,28)(22,34)(23,35)(24,36)(25,37)(26,31)(30,39)(32,38)(33,40);(9,12,14,23)(10,16,18,31)(11,19,21,35)(13,24,25,22)(15,26,28,29)(17,32,33,30)(20,36,37,34)(27,39,40,38);(2,6)(5,7)(9,13,14,25)(10,17,18,33)(11,20,21,37)(12,22,23,24)(15,27,28,40)(16,30,31,32)(19,34,35,36)(26,38,29,39)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16977);