Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| isoclinism | isoclinic class of C43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C43⋊C7 |
| unambiguous semidirect product | (C2×C32×C43)⋊C7 |
| Fitting, socle, Hall | C2×C32×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C2×C32×C7 |
| Hall | C32×C43 ⋊ C2×C7 |
| Hall | C2×C43 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C43⋊C7 |
| commutator, hypocenter | C43 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 45);