Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C22 |
| direct product | C151×#8690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #380 |
| commutator | C42 | C22×C4×C151 |
| Frattini, cosocle | C2×C42 | C23×C151 |
| prime radical | #121×C151 | Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 3 generators on 191 points:
(1,2,4,7,5,3,8,6)(9,10)(11,20)(12,25,27,32)(13,28)(14,18)(15,19)(16,22)(17,26,33,29)(21,30,37,40)(23,31)(24,35)(34,36,39,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191);(9,11,13,22,15,24,14,23)(10,16,18,20,19,31,28,35)(12,21,26,36,27,37,29,38)(17,30,32,34,33,40,25,39);(1,3)(2,5)(4,6)(7,8)(9,12)(10,17)(11,21)(13,26)(14,29)(15,27)(16,30)(18,32)(19,33)(20,34)(22,36)(23,38)(24,37)(25,28)(31,40)(35,39)6946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 1678);