Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C232⋊C9 ⋊ C2 |
| Sylow | C232 ⋊ D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C232⋊C9 | C2 |
| Frattini | C3 | #15691772 |
| Fitting, socle | C3×C232 | D3 |
| LCS | G ▷ C232⋊C9 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23^2,3|b^3=e^2,b^a=b^2e,d^a=c^2d^22,e^a=e^2,c^b=c^15d^19,d^b=c^20d^7303 conjugacy classes — view the full character table.
| maximal subgroup of | #23749009⋊C2, C2×#23749009 |
| maximal normal subgroup of | #23749009⋊C2, C2×#23749009 |
| maximal quotient of | #34039894, C2×#23749009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 12);