Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26012696 |
| Fitting, socle, derived | C3×C432 ⋊ C2×C3 |
| Hall | C3×#19149816 ⋊ 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 | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 774 |
A minimal faithful permutation representation — 2 generators on 89 points:
(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,25)(14,20,22)(16,23,19)(18,27,36)(21,29,34)(24,32,31)(26,35,28)(30,39,43)(33,40,42)(37,44,38)(41,45,46)(48,52,53,49,50,54)(51,60,61,55,56,70)(57,73,74,63,64,83)(58,72,68,66,62,59)(65,75,80,67,76,86)(69,71,85,77,78,81)(79,84,88,82,87,89);(1,2,3)(4,5,7,11,18,23,8,12,19,28,38,35,15,22,31,27,37,44,25,34,42,39,17,26,36,43,46,45,29,10,16,24,33,41,40,20,6,9,14,21,30,32,13)(47,48,51,57,65,66,50,54,59,69,79,78,56,62,70,80,88,87,64,75,81,83,74,85,76,73,84,89,86,61,72,60,71,82,77,68,53,52,58,67,63,55,49)Polycyclic presentation:
2,3^2,43^2|c^a=c^2,e^a=e^42,d^b=d^36,e^b=e^6954 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 53);