Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C23 |
| direct product | C2×C3×C232⋊C3 |
| unambiguous semidirect product | (C2×C232)⋊C32 |
| unambiguous semidirect product | (C2×C3×C232)⋊C3 |
| Fitting, socle | C2×C3×C232 ⋊ C3 |
| derived, Sylow | C232 ⋊ C2×C32 |
| Hall | C2×C232 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C232⋊C3 |
| commutator, cosocle, hypocenter | C232 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C232 | C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
1074 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20263650, C3×(C23⋊Dic23)⋊C3, C3⋊#20263650, … |
| maximal normal subgroup of | C3×#20263650, C3×(C23⋊Dic23)⋊C3, C3⋊#20263650, … |
| maximal quotient of | C3×C4×C232⋊C3, C22×C3×C232⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 26);