Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×(C13⋊C3)⋊D13 |
| unambiguous semidirect product | (C13⋊C3)⋊(C23×D13) |
| Fitting, socle, Hall | C132×C23 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C2×C3×C23 |
| Hall | C13×C23×C13⋊C3 ⋊ C2 |
| Hall | C23×C13⋊D13 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C2×C23 |
| Hall | C13⋊D13 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C13⋊C3)⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C132×C23 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C23 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 897 |
1150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 19);