Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C139 · Schur multiplier (H2) = C23 |
| direct product | C139×#11710 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | C2×#102 |
| commutator | C2×C8 | C22×C4×C139 |
| Frattini, cosocle | C22×C8 | C23×C139 |
| prime radical | #3050×C139 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ C23×C8×C139 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 179 |
| transitive degree | μt(G) = 8896 |
A minimal faithful permutation representation — 3 generators on 179 points:
(1,2)(3,7,8,5)(4,6)(9,10,13,18,15,20,14,19)(11,21,24,34,22,37,25,38)(12,26,28,17,30,35,29,36)(16,27,32,23,31,40,33,39)(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);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,27)(13,25)(14,24)(15,22)(17,34)(18,33)(19,32)(20,31)(21,35)(23,29)(26,37)(28,39)(30,40)(36,38);(11,22)(16,31)(21,37)(23,39)(24,25)(27,40)(32,33)(34,38)6394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 4698);