Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C151 · Schur multiplier (H2) = C22 |
| direct product | C151×#11640 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C151 | C2×D4 |
| commutator | C2×C4 | C22×C8×C151 |
| Frattini, cosocle | C4×C8 | C23×C151 |
| socle | C22×C151 | C2×C22⋊C8 |
| prime radical | C23×C151 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C151 ◁ C2×C4×C8×C151 ◁ G | |
296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 3 generators on 199 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,12)(11,15)(13,16)(17,18,20,25,21,26,30,38,22,24,31,36,32,37,42,46)(19,23,28,33,29,34,41,43,27,35,39,44,40,45,47,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199);(1,3,6,13)(2,7,9,15)(4,12,5,11)(8,16,14,10)(17,19)(18,23)(20,28)(21,29)(22,27)(24,35)(25,33)(26,34)(30,41)(31,39)(32,40)(36,44)(37,45)(38,43)(42,47)(46,48);(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,10,15,16)(18,24)(19,27)(25,36)(26,37)(28,39)(29,40)(38,46)(41,47)9664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 4628);