Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#12768 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #1790 |
| commutator | C2×D4 | C22×C4×C151 |
| Frattini, cosocle | C22×D4 | C23×C151 |
| prime radical | #3545×C151 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C23×C151 ◁ C22×D4×C151 ◁ G | |
778 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 4832 |
A minimal faithful permutation representation — 3 generators on 183 points:
(1,2)(3,11)(4,15,17,8)(5,18,19,9)(6,10)(7,13,21,28)(12,24,27,31)(14,25)(16,22)(20,26)(23,30)(29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(1,3,6,14)(2,7,10,21)(4,12,17,27)(5,13,19,28)(8,20,15,29)(9,11,18,25)(16,26,30,32)(22,31,23,24);(1,4)(2,8)(3,12)(5,16)(6,17)(7,20)(9,23)(10,15)(11,24)(13,26)(14,27)(18,22)(19,30)(21,29)(25,31)(28,32)5134 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5756);