Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#12939 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C151 | C2×D8 |
| commutator | C2×C8 | C22×C4×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C22×C151 | C4×D8 |
| prime radical | C2×#135×C151 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C151 ◁ C22×C8×C151 ◁ C2×C4×C8×C151 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 187 points:
(1,2)(3,4)(5,6,11,17,12,19,30,18)(7,20,24,36,26,14,25,35)(8,27,22,13,28,33,23,34)(9,29,21,15,10,31,32,16)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187);(2,4)(5,7,11,24,12,26,30,25)(6,13,17,33,19,34,18,27)(8,21,22,10,28,32,23,9)(14,16,35,29,20,15,36,31);(5,8)(6,14)(7,21)(9,25)(10,24)(11,22)(12,28)(13,16)(15,34)(17,35)(18,36)(19,20)(23,30)(26,32)(27,31)(29,33)8758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5927);