Finite Group DatabasebetaFinite Group Databasebeta| order | 1548 |
| isoclinism | isoclinic class of C3⋊D3×D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D43 |
| unambiguous semidirect product | (C3×D43)⋊D3 |
| Fitting, socle, derived, Hall | C32×C43 ⋊ C22 |
| Sylow | C43 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C43 | C22 |
| LCS | G ▷ C32×C43 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 387 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D43⋊C7, C7×C3⋊D3×D43, D43×C3⋊D21, … |
| maximal normal subgroup of | C3⋊D3×D43⋊C7, C7×C3⋊D3×D43, C11×C3⋊D3×D43, … |
| maximal quotient of | C7×C3⋊D3×D43, D43×C3⋊D21, C3⋊D3×D301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1548, 34);