Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C25 |
| direct product | C139×#24030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C139 |
| prime radical | #3489×C139 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G | |
1280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 8896 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,19)(12,17)(13,16)(14,18)(15,21)(20,24)(22,23)(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);(2,5)(6,8)(9,11,12,21)(10,15,17,19)(13,22,14,20)(16,24,18,23);(1,3,4,7)(2,6,5,8)(10,16)(11,20)(13,14)(17,18)(21,22)(23,24);(2,5)(6,8)(10,17)(15,19)(16,18)(23,24)5977 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 17018);