Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D495 |
| unambiguous semidirect product | C5⋊(C19×D99) |
| unambiguous semidirect product | C9⋊(C19×D55) |
| unambiguous semidirect product | C11⋊(C19×D45) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D495 |
| commutator, cosocle, hypocenter | C5×C9×C11 | C2×C19 |
| Frattini | C3 | C19×D165 |
| Fitting | C5×C9×C11×C19 | C2 |
| socle | C3×C5×C11×C19 | D3 |
| LCS | G ▷ C5×C9×C11 | |
| UCS | C1 ◁ C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
4731 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D495, C19×D11×D45, D209⋊D45, … |
| maximal normal subgroup of | D19×D495, C19×D11×D45, D209⋊D45, … |
| maximal quotient of | C19×Dic495, C2×C19×D495 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 18);