Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C27 |
| direct product | C151×#23875 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G | |
1642 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)(3,13)(4,9)(5,18)(6,21)(7,12)(8,15)(10,19)(11,23)(14,24)(16,32)(17,25)(20,28)(22,27)(26,31)(29,30)(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);(1,3,7,4)(2,8,12,25)(5,14,20,16)(6,17,23,15)(9,21,13,11)(10,24,27,32)(18,29,28,26)(19,31,22,30);(1,4,7,3)(2,9,12,13)(5,16,20,14)(6,15,23,17)(8,11,25,21)(10,26,27,29)(18,24,28,32)(19,30,22,31);(1,5)(2,10)(3,14)(4,16)(6,22)(7,20)(8,24)(9,26)(11,28)(12,27)(13,29)(15,31)(17,30)(18,21)(19,23)(25,32)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16863);