Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013844 |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×#14584115 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ Dic3×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150311 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×#14584115 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 11172 |
A minimal faithful permutation representation — 3 generators on 40 points:
(2,3)(4,5,6,7)(9,10,11)(12,14,13)(16,17,18)(19,21,20)(23,27,28,24,25,29)(26,35,32,30,31,37)(33,38,40,39,36,34);(1,2,3)(15,16,17,19,18,20,21)(22,23,26,32,38,35,39,25,29,34,40,28,27,33,31,36,37,30,24);(8,9,10,12,11,13,14)Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,c^a=c^2,f^a=f^18,d^b=d^2,e^b=e^2,f^b=f^7996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 729);