Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C151 · Schur multiplier (H2) = C26 |
| direct product | C151×#22412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C151 |
| Frattini, cosocle | C22×C4 | C24×C151 |
| prime radical | C2×#550×C151 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C4×D4×C151 ◁ G | |
1462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 171 points:
(2,4)(5,6,9,14,10,13,7,11)(8,16,15,20,17,12,18,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(1,2)(3,4)(5,7,10,9)(6,11,13,14)(8,15,17,18)(12,19,16,20);(5,8,10,17)(6,12,13,16)(7,15,9,18)(11,19,14,20);(2,4)(5,7,10,9)(6,11,13,14)(8,15,17,18)(12,19,16,20)8305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 15400);