Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C13 |
| direct product | C23×C3⋊(C13⋊D13) |
| unambiguous semidirect product | C3⋊(C23×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C23×D39) |
| Fitting, socle, Hall | C3×C132×C23 ⋊ C2 |
| derived, Hall | C3×C132 ⋊ C2×C23 |
| Hall | C132×C23 ⋊ D3 |
| Sylow | C132 ⋊ D3×C23 |
| Hall | C3×C23 ⋊ C13⋊D13 |
| Sylow | C3 ⋊ C23×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C3×C132 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C23 | C2 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C23 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11661 |
5865 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 45);