Finite Group DatabasebetaFinite Group Databasebeta| order | 7434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D413 |
| unambiguous semidirect product | C59⋊(C32×D7) |
| Fitting, socle, Hall | C32×C7×C59 ⋊ C2 |
| derived, Hall | C7×C59 ⋊ C2×C32 |
| Hall | C32×C59 ⋊ D7 |
| Hall | C32×C7 ⋊ D59 |
| Sylow | C59 ⋊ C32×D7 |
| Sylow | C7 ⋊ C32×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D413 |
| commutator, hypocenter | C7×C59 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C59 | C2 |
| LCS | G ▷ C7×C59 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
1872 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D7×D59, C3×D3×D413, C3×D21⋊D59, … |
| maximal normal subgroup of | C32×D7×D59, C3×D3×D413, C3×D21⋊D59, … |
| maximal quotient of | C32×Dic413, C2×C32×D413, C32×C5×D413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7434, 24);