Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C27 |
| direct product | C139×#23905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C139 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C139 |
| prime radical | #3485×C139 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G | |
1744 conjugacy classes of subgroups.
| minimal degree | μ(G) = 175 |
| transitive degree | μt(G) = 8896 |
A minimal faithful permutation representation — 4 generators on 175 points:
(5,6,10,14)(7,11,17,24)(8,12,19,26)(9,20,21,13)(15,27,29,22)(16,30,31,23)(18,25,32,33)(28,35,36,34)(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);(1,2)(3,4)(5,7,10,17)(6,11,14,24)(8,15,19,29)(9,16,21,31)(12,22,26,27)(13,23,20,30)(18,28,32,36)(25,34,33,35);(2,4)(5,8)(6,12)(7,15)(9,18)(10,19)(11,22)(13,25)(14,26)(16,28)(17,29)(20,33)(21,32)(23,34)(24,27)(30,35)(31,36);(5,9)(6,13)(7,16)(8,18)(10,21)(11,23)(12,25)(14,20)(15,28)(17,31)(19,32)(22,34)(24,30)(26,33)(27,35)(29,36)5560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 16893);