Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C26 |
| direct product | C139×#33556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C139 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C2×#41×C139 ◁ G | |
1134 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)(3,13)(4,9)(5,10)(6,11)(7,12)(8,15)(14,27)(16,28)(17,23)(18,32)(19,25)(20,26)(21,29)(22,31)(24,30)(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);(1,3,7,16)(2,8,12,22)(4,14,5,18)(6,15,20,31)(9,21,10,24)(11,13,26,28)(17,29,19,30)(23,27,25,32);(1,4,7,5)(2,9,12,10)(3,14,16,18)(6,19,20,17)(8,21,22,24)(11,23,26,25)(13,27,28,32)(15,30,31,29);(1,5,7,4)(2,10,12,9)(3,14,16,18)(6,19,20,17)(8,21,22,24)(11,25,26,23)(13,27,28,32)(15,29,31,30)4726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26544);