Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#33676 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| prime radical | C2×#135×C131 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G | |
548 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)(3,6)(4,5)(7,8)(9,10,15,20)(11,16,24,32)(12,18,14,28)(13,17,27,34)(19,25,33,26)(21,30,23,38)(22,29,37,40)(31,35,39,36)(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);(2,5)(6,8)(9,11,15,24)(10,16,20,32)(12,21,14,23)(13,22,27,37)(17,29,34,40)(18,30,28,38)(19,31,33,39)(25,35,26,36);(10,17)(12,14)(13,26)(16,29)(18,19)(20,34)(21,23)(22,36)(25,27)(28,33)(30,31)(32,40)(35,37)(38,39);(1,3,4,7)(2,6,5,8)(9,12,15,14)(10,18,20,28)(11,21,24,23)(13,25,27,26)(16,30,32,38)(17,33,34,19)(22,35,37,36)(29,39,40,31)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26664);