Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11759817 |
| Fitting, socle, derived, Hall | C132×C23 ⋊ C2×C3 |
| Hall | C23×#92788 ⋊ C2 |
| Hall | C13×D299 ⋊ C3 |
| Hall | #92788 ⋊ D23 |
| Sylow | C132 ⋊ C3×D23 |
| Sylow | C23 ⋊ #11759817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C23 | C2×C3 |
| LCS | G ▷ C132×C23 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 598 |
Polycyclic presentation:
2,3,13^2,23|c^a=c^12,e^a=e^22,c^b=c^3,d^b=d^3689 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 27);