Finite Group DatabasebetaFinite Group Databasebeta| order | 1032 |
| isoclinism | isoclinic class of D43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C3×C4) |
| unambiguous semidirect product | (C4×D43)⋊C3 |
| Fitting | C4×C43 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C3×C4 |
| Hall | C4×D43 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C3×C4 |
| Frattini | C2 | C2×D43⋊C3 |
| Fitting | C4×C43 | C2×C3 |
| socle, cosocle | C2×C43 | C22×C3 |
| prime radical | C2×D43⋊C3 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 172 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D43⋊C3, C4×AGL(1,𝔽43), AGL(1,𝔽5)×D43⋊C3 |
| maximal normal subgroup of | D4×D43⋊C3, C4×AGL(1,𝔽43) |
| maximal quotient of | AGL(1,𝔽5)×D43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1032, 8);