Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C139 · Schur multiplier (H2) = C25 |
| direct product | C139×#33455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | C22×D8 |
| commutator | C8 | C23×C4×C139 |
| Frattini, cosocle | C2×C8 | C24×C139 |
| prime radical | C2×#135×C139 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ #117×C139 ◁ #405×C139 ◁ G | |
660 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)(6,11)(8,18)(9,20)(12,24)(13,28)(14,25)(16,31)(17,30)(19,22)(21,23)(26,35)(27,36)(29,34)(32,33)(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);(5,6,10,14)(7,12,15,26)(8,19,21,28)(9,22,20,13)(11,23,25,18)(16,32,29,36)(17,33,30,27)(24,34,35,31);(1,3,4,2)(5,7)(6,12)(8,16)(9,17)(10,15)(11,24)(13,27)(14,26)(18,31)(19,32)(20,30)(21,29)(22,33)(23,34)(25,35)(28,36);(7,15)(12,26)(16,29)(17,30)(24,35)(27,33)(31,34)(32,36)8896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26443);