Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#24809 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G | |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 4832 |
A minimal faithful permutation representation — 4 generators on 183 points:
(1,2,5,10,6,11,19,9)(3,12,15,7,17,13,16,23)(4,18,20,8,21,24,32,25)(14,28,29,26,31,22,30,27)(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);(1,3,5,15,6,17,19,16)(2,7,9,12,11,23,10,13)(4,14,20,29,21,31,32,30)(8,22,18,26,25,28,24,27);(1,2)(3,13)(4,8)(5,9)(6,11)(7,15)(10,19)(12,17)(14,27)(16,23)(18,20)(21,25)(22,29)(24,32)(26,31)(28,30);(1,4,19,32,6,21,5,20)(2,8,10,24,11,25,9,18)(3,14,16,30,17,31,15,29)(7,22,13,27,23,28,12,26)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 17797);