Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C19×C53 ⋊ C2×C3 |
| derived, Hall | C19×C53 ⋊ C2×C32 |
| Hall | C3×C53×C19⋊C3 ⋊ C2 |
| Hall | D1007 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ C3×D19⋊C3 |
| Sylow | C19 ⋊ C32×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C53⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C19×C53 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C53 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D53×D19⋊C3, D3×C53⋊(D19⋊C3), D159⋊(D19⋊C3), … |
| maximal normal subgroup of | C3×D53×D19⋊C3, D3×C53⋊(D19⋊C3), D159⋊(D19⋊C3), … |
| maximal quotient of | C3×(C19⋊C3)⋊Dic53, C2×C3×C53⋊(D19⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 19);