Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#26012691 |
| Fitting, socle | C3×C432 ⋊ D3 |
| derived, Hall | C3×#19149816 ⋊ C2 |
| Sylow | C432 ⋊ C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#19149816 | C2 |
| Fitting, socle | C3×C432 | D3 |
| LCS | G ▷ C3×#19149816 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 258 |
A minimal faithful permutation representation — 3 generators on 89 points:
(2,3)(4,10,21,31,57,70,74,89,54,83,36,68,22,46,13,18,39,50,78,85,87,86,76,72,58,33,40,66,25,32,61,71,88,75,77,52,55,19,28,67,62,82,43,51,79,56,59,34,37,11,16,47,73,80,81,60,63,38,41,20,23,7,9,30,53,64,65,42,44,24,26,12,14,5,6,17,35,49,45,84,27,69,15,48,8,29);(1,2,3);(6,8,13)(7,10,12)(9,15,25)(11,18,24)(14,22,21)(16,27,43)(17,29,20)(19,32,42)(23,36,39)(26,40,35)(28,45,63)(30,46,38)(31,48,34)(33,51,64)(37,54,61)(41,58,57)(44,62,53)(47,66,60)(49,68,56)(50,69,52)(55,74,79)(59,76,78)(65,81,73)(67,82,80)(70,83,75)(71,84,72)(77,87,88)(85,89,86)Polycyclic presentation:
2,3^2,43^2|b^a=b^2,c^a=c^2,d^a=e,e^a=d,d^b=d^36,e^b=e^6993 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 47);