Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C2×C4 |
| direct product | C151×#8681 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #380 |
| commutator | C42 | C22×C4×C151 |
| Frattini, cosocle | C2×C42 | C23×C151 |
| prime radical | C23×C151 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 199 points:
(1,2)(3,9)(4,6)(5,13)(7,11)(8,12)(10,16)(14,15)(17,18)(19,28)(20,33,35,40)(21,36)(22,26)(23,27)(24,30)(25,34,41,37)(29,38,45,48)(31,39)(32,43)(42,44,47,46)(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);(2,6)(7,15)(8,13)(9,16)(17,19,22,31,23,32,21,30)(18,24,36,43,27,39,26,28)(20,29,37,46,35,45,34,44)(25,38,33,47,41,48,40,42);(1,3,4,10)(2,7,6,15)(5,14,12,11)(8,16,13,9)(17,20)(18,25)(19,29)(21,34)(22,37)(23,35)(24,38)(26,40)(27,41)(28,42)(30,44)(31,46)(32,45)(33,36)(39,48)(43,47)6946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 1669);