Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#12786 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C151 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C22×C151 | C2×C22⋊C8 |
| prime radical | C24×C151 | C2×C8 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C151 ◁ C2×C4×C8×C151 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 187 points:
(2,4)(5,6,8,13,9,14,19,26,10,12,18,24,20,25,30,34)(7,11,16,22,17,23,29,33,15,21,27,31,28,32,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187);(1,2,3,4)(5,7)(6,11)(8,16)(9,17)(10,15)(12,21)(13,22)(14,23)(18,27)(19,29)(20,28)(24,31)(25,32)(26,33)(30,35)(34,36);(6,12)(7,15)(8,18)(14,25)(17,28)(19,30)(22,31)(33,36)9664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5774);