Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C19 · Schur multiplier (H2) = C2×C3 |
| direct product | C19×#3861⋊A4 |
| unambiguous semidirect product | #3861⋊(A4×C19) |
| Fitting, socle, Hall | C22×C72×C19 ⋊ C32 |
| derived, Hall | C22×C72 ⋊ C32×C19 |
| Hall | C72×C19 ⋊ C3×A4 |
| Hall | C22×C19 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C72 ⋊ C3×A4×C19 |
| Sylow | C22 ⋊ C19×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #3861⋊A4 |
| commutator, cosocle, hypocenter | C22×C72 | C32×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C32 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C19 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
836 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1304);