Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C26 |
| direct product | C139×#33533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C139 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G | |
1102 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)(4,9)(5,18)(6,16)(7,11)(8,14)(10,21)(13,29)(15,30)(17,20)(19,24)(22,31)(23,27)(25,28)(26,32)(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)(5,19)(6,23)(7,15)(9,24)(10,27)(11,25)(12,18)(14,21)(16,26)(17,28)(20,29)(22,32)(30,31);(1,2)(3,8)(4,16)(5,20)(6,9)(7,11)(10,22)(12,28)(13,26)(14,30)(15,25)(17,18)(19,29)(21,31)(23,24)(27,32);(1,4,7,6)(2,9,11,16)(3,13,15,23)(5,17,22,21)(8,24,25,26)(10,18,20,31)(12,29,30,27)(14,19,28,32)5560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26521);