Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#23542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C151 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C151 |
| prime radical | C24×C151 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G | |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 191 |
| transitive degree | μt(G) = 19328 |
A minimal faithful permutation representation — 4 generators on 191 points:
(1,2)(3,4)(9,10,15,20)(11,21,25,32)(12,26,28,36)(13,19,14,18)(16,24,33,23)(17,30,35,29)(22,38,39,31)(27,34,40,37)(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);(5,6)(7,8)(9,11,15,25)(10,16,20,33)(12,27,28,40)(13,24,14,23)(17,34,35,37)(18,32,19,21)(22,29,39,30)(26,38,36,31);(2,4)(6,8)(9,12,13,29,15,28,14,30)(10,17,18,26,20,35,19,36)(11,22,23,40,25,39,24,27)(16,31,21,37,33,38,32,34);(12,28)(17,35)(22,39)(26,36)(27,40)(29,30)(31,38)(34,37)7852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 16530);