Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C23 |
| unambiguous semidirect product | C3⋊(C3⋊(C23⋊D23)) |
| unambiguous semidirect product | C23⋊(C3⋊D69) |
| Fitting, socle, derived, Hall | C32×C232 ⋊ C2 |
| Sylow | C232 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C232 | C2 |
| LCS | G ▷ C32×C232 | |
| UCS | C1 | |
312 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,23^2|b^a=b^2,c^a=c^2,d^a=d^22,e^a=e^222382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×C23⋊D23, D23×C3⋊D69, D3×C3⋊(C23⋊D23), … |
| maximal normal subgroup of | C3⋊D3×C23⋊D23, D23×C3⋊D69, D3×C3⋊(C23⋊D23), … |
| maximal quotient of | C3⋊(C3⋊(C23⋊Dic23)), C2×C3⋊(C3⋊(C23⋊D23)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 34);