Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×C11×D19 |
| Fitting, Hall | C5×C9×C11×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C5×C9×C11 |
| Hall | C9×C11×C19 ⋊ C2×C5 |
| Hall | C5×C11×C19 ⋊ C2×C9 |
| Hall | C5×C9×C19 ⋊ C2×C11 |
| Hall | C11×C19 ⋊ C2×C5×C9 |
| Hall | C9×C19 ⋊ C2×C5×C11 |
| Hall | C5×C19 ⋊ C2×C9×C11 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
5445 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×D11×D19, C9×D5×C11×D19, C9×D19×D55, … |
| maximal normal subgroup of | C5×C9×D11×D19, C9×D5×C11×D19, C9×D19×D55, … |
| maximal quotient of | C5×C9×C11×Dic19, C2×C5×C9×C11×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 5);