Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#15691772 |
| Fitting, socle | C3×C232 ⋊ D3 |
| derived, Hall | C3×C232⋊C3 ⋊ C2 |
| Sylow | C232 ⋊ C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C232⋊C3 | C2 |
| Fitting, socle | C3×C232 | D3 |
| LCS | G ▷ C3×C232⋊C3 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,23^2|b^a=b^2,c^a=c^2,e^a=d^2e^22,d^b=d^7e^4,e^b=d^3e^15303 conjugacy classes — view the full character table.
| maximal subgroup of | #15691772⋊D3, ((C23⋊D23)⋊C3)⋊D3, D3×#15691772, … |
| maximal normal subgroup of | #15691772⋊D3, ((C23⋊D23)⋊C3)⋊D3, D3×#15691772, … |
| maximal quotient of | C3⋊#20263650, C2×C3⋊#15691772 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 23);