Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#12734 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C151 | C2×D8 |
| commutator | C2×C8 | C22×C4×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C22×C151 | C2×#102 |
| prime radical | C22×#135×C151 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C151 ◁ C23×C4×C151 ◁ C23×C8×C151 ◁ G | |
932 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 187 points:
(1,2)(3,4)(5,6,9,14,11,15,10,25)(7,16,18,32,19,33,26,30)(8,20,22,31,24,35,23,13)(12,21,27,34,29,36,28,17)(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);(5,7)(6,12)(8,21)(9,18)(10,26)(11,19)(13,30)(14,27)(15,29)(16,20)(17,23)(22,34)(24,36)(25,28)(31,32)(33,35);(2,4)8758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5722);