Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×C3⋊D159 |
| unambiguous semidirect product | C3⋊(C19×D159) |
| unambiguous semidirect product | C53⋊(C3⋊D3×C19) |
| Fitting, socle, Hall | C32×C19×C53 ⋊ C2 |
| derived, Hall | C32×C53 ⋊ C2×C19 |
| Hall | C19×C53 ⋊ C3⋊D3 |
| Hall | C32×C19 ⋊ D53 |
| Sylow | C53 ⋊ C3⋊D3×C19 |
| Sylow | C32 ⋊ C19×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊D159 |
| commutator, cosocle, hypocenter | C32×C53 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C53 | C2 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 ◁ C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
4560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#14274231, C19⋊#14274231, D3×C19×D159, … |
| maximal normal subgroup of | C19×#14274231, C19⋊#14274231, D3×C19×D159, … |
| maximal quotient of | C19×C3⋊Dic159, C2×C19×C3⋊D159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 28);