Finite Group DatabasebetaFinite Group Databasebeta| order | 9090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D9×C101⋊C5 |
| unambiguous semidirect product | C9⋊(C2×C101⋊C5) |
| unambiguous semidirect product | (D9×C101)⋊C5 |
| Fitting, derived, Hall | C9×C101 ⋊ C2×C5 |
| Hall | C9×C101⋊C5 ⋊ C2 |
| Hall | D9×C101 ⋊ C5 |
| Sylow | C101 ⋊ C5×D9 |
| Sylow | C9 ⋊ C2×C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C101 | C2×C5 |
| Frattini | C3 | D3×C101⋊C5 |
| socle | C3×C101 | C5×D3 |
| LCS | G ▷ C9×C101 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D101⋊C5, C2×D9×C101⋊C5 |
| maximal normal subgroup of | D9×D101⋊C5, C2×D9×C101⋊C5 |
| maximal quotient of | Dic9×C101⋊C5, C2×D9×C101⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9090, 11);