Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013820 |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×#14584116 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ Dic3×C19⋊C3 |
| Sylow | C19 ⋊ C3⋊#10596874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150287 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×#14584116 | 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)(9,12,13,10,11,14)(16,19,20,17,18,21)(23,24,26)(25,28,32)(27,30,29)(31,35,36)(33,37,34)(38,40,39);(1,2,3)(15,16,18,21,20,19,17)(22,23,25,28,33,38,37,26,29,34,35,24,27,31,32,36,39,40,30);(8,9,11,14,13,12,10)Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,c^a=c^2,d^a=d^6,e^a=e^6,d^b=d^2,e^b=e^2,f^b=f^11966 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 704);