Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| direct product | D23×(C11⋊D11)⋊C3 |
| unambiguous semidirect product | (D23×C11⋊D11)⋊C3 |
| Fitting, socle, derived, Hall | C112×C23 ⋊ C22×C3 |
| Hall | D23×C11⋊D11 ⋊ C3 |
| Hall | C23×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ C2×D23 |
| Sylow | C112 ⋊ C2×C3×D23 |
| Sylow | C23 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C23 | C22×C3 |
| LCS | G ▷ C112×C23 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 78);