Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D9×C19 |
| unambiguous semidirect product | C9⋊(C2×C5×C11×C19) |
| Fitting, Hall | C5×C9×C11×C19 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C5×C11×C19 |
| Hall | C9×C11×C19 ⋊ C2×C5 |
| Hall | C5×C9×C19 ⋊ C2×C11 |
| Hall | C5×C9×C11 ⋊ C2×C19 |
| Hall | C9×C19 ⋊ C2×C5×C11 |
| Hall | C9×C11 ⋊ C2×C5×C19 |
| Hall | C5×C9 ⋊ C2×C11×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11×C19 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C5×C11×C19 |
| Frattini | C3 | C5×D3×C11×C19 |
| Fitting | C5×C9×C11×C19 | C2 |
| socle | C3×C5×C11×C19 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C5×C11×C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
6270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×D9×D19, C5×D9×C19×D11, C5×D9×D209, … |
| maximal normal subgroup of | C5×C11×D9×D19, C5×D9×C19×D11, C5×D9×D209, … |
| maximal quotient of | C5×C11×C19×Dic9, C2×C5×C11×D9×C19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 12);