Finite Group DatabasebetaFinite Group Databasebeta| order | 1548 |
| isoclinism | isoclinic class of D9×D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D43 |
| unambiguous semidirect product | (D9×C43)⋊C2 |
| unambiguous semidirect product | (C9×D43)⋊C2 |
| unambiguous semidirect product | D387⋊C2 |
| Fitting, derived, Hall | C9×C43 ⋊ C22 |
| Sylow | C43 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C43 | C22 |
| Frattini | C3 | D3×D43 |
| socle | C3×C43 | C2×D3 |
| LCS | G ▷ C9×C43 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 52 |
| transitive degree | μt(G) = 387 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D43⋊C7, C7×D9×D43, D43×D63, … |
| maximal normal subgroup of | D9×D43⋊C7, C7×D9×D43, C11×D9×D43, … |
| maximal quotient of | C7×D9×D43, D43×D63, D9×D301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1548, 8);