Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#23520 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C151 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| socle | C22×C151 | C2×#121 |
| prime radical | C22×#135×C151 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C151 ◁ C23×C4×C151 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 187 points:
(1,2)(3,4)(5,6)(7,16)(8,20)(9,14)(10,25)(11,15)(12,18)(13,24)(17,33)(19,28)(21,32)(22,35)(23,31)(26,29)(27,36)(30,34)(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);(5,7)(6,12)(8,21)(9,18)(10,26)(11,19)(13,30)(14,28)(15,29)(16,25)(17,24)(20,27)(22,36)(23,34)(31,32)(33,35);(2,4)(5,8,10,23,11,24,9,22)(6,13,14,31,15,20,25,35)(7,17,18,34,19,21,26,36)(12,27,16,32,29,30,28,33);(5,9,11,10)(6,14,15,25)(7,18,19,26)(8,22,24,23)(12,28,29,16)(13,31,20,35)(17,34,21,36)(27,33,30,32)7852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16508);