Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#33770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×#41×C131 ◁ C2×#131×C131 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,19)(11,22,24,16)(12,21,15,18)(14,29,28,32)(17,35,36,25)(20,27,38,31)(23,33,26,37)(30,39,40,34)(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)(2,5)(4,8)(6,7)(9,11,13,24)(10,16,19,22)(12,26,15,23)(14,25,28,35)(17,29,36,32)(18,37,21,33)(20,34,38,39)(27,40,31,30);(3,8)(5,7)(9,11)(10,17)(12,23)(13,24)(14,30)(15,26)(16,32)(18,34)(19,36)(20,37)(21,39)(22,29)(25,31)(27,35)(28,40)(33,38);(2,6)(5,7)(9,12,13,15)(10,18,19,21)(11,23,24,26)(14,27,28,31)(16,33,22,37)(17,34,36,39)(20,32,38,29)(25,30,35,40)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26758);