Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C24 |
| direct product | C151×#19407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C151 |
| prime radical | C23×C151 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 4 generators on 199 points:
(1,2,6,9)(3,10,13,16)(4,8,5,14)(7,11,15,12)(17,18,22,26)(19,23,28,37)(20,30,32,40)(21,33,35,25)(24,34,39,31)(27,41,42,48)(29,45,44,38)(36,46,47,43)(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);(1,3,5,12,6,13,4,11)(2,7,8,10,9,15,14,16)(17,19)(18,23)(20,27)(21,29)(22,28)(24,36)(25,38)(26,37)(30,41)(31,43)(32,42)(33,45)(34,46)(35,44)(39,47)(40,48);(17,20,22,32)(18,24,26,39)(19,27,28,42)(21,34,35,31)(23,36,37,47)(25,40,33,30)(29,46,44,43)(38,48,45,41);(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,10,15,16)(19,28)(23,37)(27,42)(29,44)(36,47)(38,45)(41,48)(43,46)7399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 12395);