Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#24473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G | |
1314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 4832 |
A minimal faithful permutation representation — 4 generators on 183 points:
(1,2,7,11,8,5,6,23)(3,12,15,9,17,26,16,14)(4,18,21,20,22,28,24,10)(13,30,31,27,32,25,19,29)(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)(2,9)(4,19)(5,14)(6,16)(7,15)(8,17)(10,27)(11,26)(12,23)(13,21)(18,25)(20,29)(22,31)(24,32)(28,30);(1,4)(2,10)(3,13)(5,20)(6,21)(7,24)(8,22)(9,25)(11,28)(12,29)(14,30)(15,19)(16,31)(17,32)(18,23)(26,27);(1,5,8,2)(3,14,17,9)(4,20,22,10)(6,11,7,23)(12,16,26,15)(13,30,32,25)(18,21,28,24)(19,29,31,27)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 17461);