Finite Group DatabasebetaFinite Group Databasebeta| order | 9495 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C211⋊C5 |
| unambiguous semidirect product | (C9×C211)⋊C5 |
| Fitting, Hall | C9×C211 ⋊ C5 |
| derived, Sylow | C211 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C211⋊C5 |
| commutator, hypocenter | C211 | C5×C9 |
| Frattini | C3 | C3×C211⋊C5 |
| Fitting | C9×C211 | C5 |
| socle, cosocle | C3×C211 | C3×C5 |
| prime radical | C3×C211⋊C5 | C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
423 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×C211⋊C5, C9×D211⋊C5, D9×C211⋊C5, … |
| maximal normal subgroup of | C2×C9×C211⋊C5, C9×D211⋊C5, D9×C211⋊C5, … |
| maximal quotient of | C2×C9×C211⋊C5, C22⋊C9×C211⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9495, 3);