Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C24 |
| direct product | C151×#13021 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C151 | #447 |
| commutator | C2×C8 | C22×C4×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C2×C151 | #1879 |
| prime radical | #3414×C151 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 215 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 215 points:
(1,2,7,14,8,15,31,46,9,16,6,13,30,45,5,12)(3,17,20,39,21,44,19,49,22,47,29,10,34,37,32,38)(4,23,26,50,27,48,24,11,28,41,25,42,35,40,33,43)(18,52,54,59,55,36,60,61,56,62,57,64,58,63,53,51)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215);(1,3,8,34,9,22,30,21)(2,10,15,49,16,39,45,38)(4,18,35,55,28,56,27,58)(5,29,7,19,31,20,6,32)(11,36,50,62,43,63,42,52)(12,44,14,17,46,37,13,47)(23,59,40,61,41,64,48,51)(24,54,26,60,33,57,25,53);(1,4)(2,11)(3,18)(5,26)(6,24)(7,33)(8,35)(9,28)(10,36)(12,41)(13,40)(14,48)(15,50)(16,43)(17,51)(19,57)(20,53)(21,58)(22,56)(23,46)(25,31)(27,30)(29,60)(32,54)(34,55)(37,59)(38,52)(39,63)(42,45)(44,64)(47,61)(49,62)6946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6009);