Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#10624391⋊C2 |
| unambiguous semidirect product | #10624391⋊(C2×C23) |
| unambiguous semidirect product | ((C11⋊D11)⋊C3)⋊(C2×C23) |
| Fitting, socle, Hall | C112×C23 ⋊ C2×D3 |
| derived, Hall | C112⋊C3 ⋊ C22×C23 |
| Hall | C23×C112⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C2×D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10624391⋊C2 |
| commutator, cosocle, hypocenter | C112⋊C3 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | C2×D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C23 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
713 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 83);