Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D169⋊C3 |
| unambiguous semidirect product | D169⋊(C3×C23) |
| unambiguous semidirect product | (C169⋊C3)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D169)⋊C3 |
| Fitting, Hall | C23×C169 ⋊ C2×C3 |
| derived, Sylow | C169 ⋊ C2×C3×C23 |
| Hall | C23×C169⋊C3 ⋊ C2 |
| Hall | C23×D169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C2×C23 |
| Hall | D169 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C2×C3×C23 |
| Frattini | C13 | C23×D13⋊C3 |
| Fitting | C23×C169 | C2×C3 |
| socle | C13×C23 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3887 |
782 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 3);