Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C139 · Schur multiplier (H2) = C25 |
| direct product | C139×#33460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | C22×D8 |
| commutator | C8 | C23×C4×C139 |
| Frattini, cosocle | C2×C8 | C24×C139 |
| prime radical | C2×#508×C139 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ #117×C139 ◁ #405×C139 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 175 |
| transitive degree | μt(G) = 17792 |
A minimal faithful permutation representation — 4 generators on 175 points:
(1,2,4,3)(5,6,11,17)(7,19,8,14)(9,18,12,15)(10,25,27,33)(13,23,30,21)(16,24,34,28)(20,31,22,32)(26,35,36,29)(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);(5,7,11,8)(6,13,17,30)(9,20,12,22)(10,26,27,36)(14,25,19,33)(15,29,18,35)(16,32,34,31)(21,24,23,28);(1,3,4,2)(5,8,11,7)(6,14,17,19)(9,20,12,22)(10,23,27,21)(13,25,30,33)(15,32,18,31)(16,29,34,35)(24,26,28,36);(5,9,11,12)(6,15,17,18)(7,20,8,22)(10,24,27,28)(13,29,30,35)(14,31,19,32)(16,33,34,25)(21,26,23,36)8896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26448);