Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D23×#92788 |
| unambiguous semidirect product | C23⋊(C2×#92788) |
| Fitting, socle, derived, Hall | C132×C23 ⋊ C2×C3 |
| Hall | C23×#92788 ⋊ C2 |
| Hall | C132×D23 ⋊ C3 |
| Sylow | C132 ⋊ C3×D23 |
| Sylow | C23 ⋊ C2×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C23 | C2×C3 |
| LCS | G ▷ C132×C23 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3887 |
767 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 23);