Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C27 |
| direct product | C151×#23917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G | |
1682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 187 points:
(5,6)(7,12)(8,20)(9,14)(10,25)(11,16)(13,23)(15,18)(17,30)(19,29)(21,36)(22,32)(24,28)(26,31)(27,34)(33,35)(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);(1,2)(3,4)(5,7,11,19)(6,12,16,29)(8,17,22,33)(9,10,24,18)(13,27,31,36)(14,25,28,15)(20,35,32,30)(21,26,34,23);(2,4)(5,8)(6,13)(7,17)(9,21)(10,26)(11,22)(12,27)(14,30)(15,32)(16,31)(18,23)(19,33)(20,25)(24,34)(28,35)(29,36);(5,9,11,24)(6,14,16,28)(7,18,19,10)(8,21,22,34)(12,15,29,25)(13,30,31,35)(17,23,33,26)(20,27,32,36)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16905);