Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C2 |
| direct product | C151×#9634 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C151 | #121 |
| commutator | C42 | C22×C4×C151 |
| Frattini, cosocle | C2×C42 | C23×C151 |
| socle | C22×C151 | #389 |
| prime radical | C23×C151 | #125 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G | |
268 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 3 generators on 183 points:
(1,2,6,9,5,8,4,13)(3,10,11,7,12,16,14,15)(18,23)(19,26)(20,21)(24,31)(25,29)(27,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(1,3,6,11,5,12,4,14)(2,7,9,16,8,15,13,10)(17,18)(19,24)(20,29)(21,23)(22,25)(26,30)(27,32)(28,31);(2,8)(7,15)(9,13)(10,16)(17,19,20,27,22,28,21,26)(18,24,29,32,25,31,23,30)8758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 2622);