Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C139 · Schur multiplier (H2) = C25 |
| direct product | C139×#33471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | C2×#442 |
| commutator | C8 | C23×C4×C139 |
| Frattini, cosocle | C2×C8 | C24×C139 |
| prime radical | C2×#509×C139 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C22×C4×C139 ◁ #405×C139 ◁ G | |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 4448 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2)(3,12,16,29)(4,18)(5,9)(6,19)(7,11)(8,15,25,32)(10,20)(13,30,24,21)(14,28,17,26)(22,23)(27,31)(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);(1,3)(2,8)(4,13)(5,14)(6,21)(7,16)(9,24)(10,26)(11,25)(12,22)(15,31)(17,18)(19,29)(20,32)(23,30)(27,28);(1,4,18,2,7,9,5,11)(3,13,17,8,16,24,14,25)(6,22,31,27,23,19,20,10)(12,15,28,30,29,32,26,21);(1,5,7,18)(2,9,11,4)(3,14,16,17)(6,20,23,31)(8,24,25,13)(10,22,27,19)(12,28,29,26)(15,21,32,30)6394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26459);