Finite Group DatabasebetaFinite Group Databasebeta| order | 18990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D211⋊C5 |
| unambiguous semidirect product | (C9×D211)⋊C5 |
| Fitting, Hall | C9×C211 ⋊ C2×C5 |
| derived, Sylow | C211 ⋊ C2×C5×C9 |
| Hall | C9×C211⋊C5 ⋊ C2 |
| Hall | C9×D211 ⋊ C5 |
| Hall | C211⋊C5 ⋊ C2×C9 |
| Hall | D211 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D211⋊C5 |
| commutator, hypocenter | C211 | C2×C5×C9 |
| Frattini | C3 | C3×D211⋊C5 |
| Fitting | C9×C211 | C2×C5 |
| socle, cosocle | C3×C211 | C2×C3×C5 |
| prime radical | C3×D211⋊C5 | C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1899 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D211⋊C5, C2×C9×D211⋊C5 |
| maximal normal subgroup of | D9×D211⋊C5, C2×C9×D211⋊C5 |
| maximal quotient of | C9×Dic211⋊C5, C2×C9×D211⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18990, 12);