Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C23⋊D23)⋊C9 |
| derived, Sylow | C232 ⋊ C2×C9 |
| Hall | C232⋊C9 ⋊ C2 |
| Hall | C23⋊D23 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C23⋊D23)⋊C3 |
| commutator, hypocenter | C232 | C2×C9 |
| Fitting, socle, cosocle | C3×C232 | C2×C3 |
| prime radical | C3×C23⋊D23 | C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23^2,3|b^3=e,c^a=c^22,d^a=d^22,c^b=c^7d^17,d^b=c^21d^15282 conjugacy classes — view the full character table.
| maximal subgroup of | #23749009⋊C2, #14523747⋊C9, #34039905, … |
| maximal normal subgroup of | #23749009⋊C2, #14523747⋊C9, #34039905, … |
| maximal quotient of | (C23⋊Dic23)⋊C9, C2×(C23⋊D23)⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 13);