Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D23×C169⋊C3 |
| unambiguous semidirect product | C23⋊(C2×C169⋊C3) |
| unambiguous semidirect product | (D23×C169)⋊C3 |
| Fitting, derived, Hall | C23×C169 ⋊ C2×C3 |
| Hall | C23×C169⋊C3 ⋊ C2 |
| Hall | D23×C169 ⋊ C3 |
| Sylow | C169 ⋊ C3×D23 |
| Sylow | C23 ⋊ C2×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C23×C169 | C2×C3 |
| Frattini | C13 | C13⋊C3×D23 |
| socle | C13×C23 | C2×C13⋊C3 |
| LCS | G ▷ C23×C169 | |
| UCS | C1 | |
24 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, 2);