Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26012697 |
| Fitting, socle, derived | C3×C432 ⋊ C2×C3 |
| Hall | C3×#19149815 ⋊ C2 |
| Sylow | C432 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C432 | C2×C3 |
| LCS | G ▷ C3×C432 | |
| UCS | C1 | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 5547 |
A minimal faithful permutation representation — 3 generators on 89 points:
(2,3)(5,9,10,6,7,11)(8,17,18,12,13,27)(14,30,31,20,21,39)(15,29,25,23,19,16)(22,35,37,26,28,40)(24,41,42,33,32,36)(34,44,45,43,38,46)(48,52,53,49,50,54)(51,60,61,55,56,70)(57,73,74,63,64,82)(58,72,68,66,62,59)(65,78,80,69,71,83)(67,84,85,76,75,79)(77,87,88,86,81,89);(1,2,3)(47,48,51,57,65,68,53,52,58,67,77,85,61,72,60,71,81,88,74,83,84,73,64,75,80,82,89,87,78,56,62,70,79,86,76,66,50,54,59,69,63,55,49);(4,5,8,14,22,25,10,9,15,24,34,42,18,29,17,28,38,45,31,40,41,30,21,32,37,39,46,44,35,13,19,27,36,43,33,23,7,11,16,26,20,12,6)Polycyclic presentation:
2,3^2,43^2|c^a=c^2,d^a=d^42,e^a=e^42,d^b=d^36,e^b=e^36933 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 55);