Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#24282 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| prime radical | #525×C151 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G | |
1308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 187 points:
(5,6,12,18)(7,19,9,27)(8,23,26,32)(10,17,11,16)(13,22,15,21)(14,28,31,25)(20,30,24,29)(33,35,36,34)(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);(1,2)(3,4)(5,7,11,22,12,9,10,21)(6,13,17,27,18,15,16,19)(8,20,28,35,26,24,25,34)(14,29,32,36,31,30,23,33);(2,4)(5,8)(6,14)(7,20)(9,24)(10,25)(11,28)(12,26)(13,29)(15,30)(16,23)(17,32)(18,31)(19,33)(21,34)(22,35)(27,36);(5,9,11,21,12,7,10,22)(6,15,17,19,18,13,16,27)(8,24,28,34,26,20,25,35)(14,30,32,33,31,29,23,36)6946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 17270);