Finite Group DatabasebetaFinite Group Databasebeta| order | 1806 |
| isoclinism | isoclinic class of C3⋊(D43⋊C7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D43⋊C7) |
| unambiguous semidirect product | D129⋊C7 |
| unambiguous semidirect product | (C43⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C43 ⋊ C2×C7 |
| Hall | C3×C43⋊C7 ⋊ C2 |
| Hall | C43⋊C7 ⋊ D3 |
| Hall | D129 ⋊ C7 |
| Sylow | C43 ⋊ D3×C7 |
| Sylow | C3 ⋊ D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C43 | C2×C7 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 129 |
Polycyclic presentation:
2,7,3,43|c^a=c^2,d^a=d^42,d^b=d^3530 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D43⋊C7, C2×C3⋊(D43⋊C7), C7×C3⋊(D43⋊C7), … |
| maximal normal subgroup of | D3×D43⋊C7, C2×C3⋊(D43⋊C7), C7×C3⋊(D43⋊C7), … |
| maximal quotient of | C3⋊(Dic43⋊C7), C2×C3⋊(D43⋊C7), C3⋊(D43⋊C49), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1806, 5);