Finite Group DatabasebetaFinite Group Databasebeta| order | 23322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11759813 |
| Fitting, socle, Hall | C132×C23 ⋊ D3 |
| derived, Hall | C23×#92789 ⋊ C2 |
| Hall | #92789 ⋊ D23 |
| Sylow | C132 ⋊ D69 |
| Sylow | C23 ⋊ #11759813 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C23×#92789 | C2 |
| Fitting, socle | C132×C23 | D3 |
| LCS | G ▷ C23×#92789 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 598 |
Polycyclic presentation:
2,3,23,13^2|b^a=b^2,c^a=c^22,d^a=d^3e^8,e^a=d^12e^10,d^b=d^9e^5,e^b=e^3698 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23322, 15);