Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C53 · Schur multiplier (H2) = C1 |
| direct product | D9×C19×C53 |
| unambiguous semidirect product | C9⋊(C2×C19×C53) |
| Fitting, Hall | C9×C19×C53 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C19×C53 |
| Hall | C9×C53 ⋊ C2×C19 |
| Hall | C9×C19 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C53 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C19×C53 |
| Frattini | C3 | D3×C19×C53 |
| Fitting | C9×C19×C53 | C2 |
| socle | C3×C19×C53 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C19×C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
6042 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C19×D53, D9×D19×C53, D9×D1007, … |
| maximal normal subgroup of | D9×C19×D53, D9×D19×C53, D9×D1007, … |
| maximal quotient of | C19×Dic9×C53, C2×D9×C19×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 6);