Finite Group DatabasebetaFinite Group Databasebeta| order | 1204 |
| isoclinism | isoclinic class of D43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D43⋊C7 |
| unambiguous semidirect product | D43⋊(C2×C7) |
| unambiguous semidirect product | (C2×D43)⋊C7 |
| unambiguous semidirect product | (C43⋊C7)⋊C22 |
| unambiguous semidirect product | (C2×C43⋊C7)⋊C2 |
| Fitting, socle | C2×C43 ⋊ C2×C7 |
| derived, Sylow | C43 ⋊ C22×C7 |
| Hall | C43⋊C7 ⋊ C22 |
| Hall | C2×D43 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 86 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽43), D3×D43⋊C7, C2×C3×D43⋊C7, … |
| maximal normal subgroup of | C2×AGL(1,𝔽43), C2×C3×D43⋊C7, C2×C13×D43⋊C7, … |
| maximal quotient of | D3×D43⋊C7, C2×C3×D43⋊C7, C2×C3⋊(D43⋊C7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1204, 7);