Finite Group DatabasebetaFinite Group Databasebeta| order | 1548 |
| isoclinism | isoclinic class of D3×D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C3×C43 ⋊ C22×C3 |
| Hall | C3×C43⋊C3 ⋊ C22 |
| Sylow | C43 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C43 | C22×C3 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 129 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽43), D3×C7×D43⋊C3, #14268588⋊D3, … |
| maximal normal subgroup of | D3×AGL(1,𝔽43), D3×C7×D43⋊C3, D3×C11×D43⋊C3, … |
| maximal quotient of | D3×C7×D43⋊C3, #14268588⋊D3, #14268587⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1548, 26);