Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#33745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| prime radical | #466×C131 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ #117×C131 ◁ #405×C131 ◁ G | |
496 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)(9,10,13,18)(11,20,24,35)(12,17,15,27)(14,30,29,37)(16,31,21,25)(19,28,33,22)(23,34,26,40)(32,38,36,39)(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)(9,10)(11,21)(12,27)(13,18)(14,19)(15,17)(16,24)(20,31)(22,30)(23,32)(25,35)(26,36)(28,37)(29,33)(34,39)(38,40);(9,11,22,38,15,26,29,31,13,24,28,39,12,23,14,25)(10,16,30,34,17,32,33,35,18,21,37,40,27,36,19,20);(1,3,4,7)(2,6,5,8)(9,12,13,15)(10,17,18,27)(11,23,24,26)(14,28,29,22)(16,32,21,36)(19,30,33,37)(20,34,35,40)(25,39,31,38)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26733);