Finite Group DatabasebetaFinite Group Databasebeta| order | 7482 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D29×C43⋊C3 |
| unambiguous semidirect product | C29⋊(C2×C43⋊C3) |
| unambiguous semidirect product | (C43×D29)⋊C3 |
| Fitting, socle, derived, Hall | C29×C43 ⋊ C2×C3 |
| Hall | C29×C43⋊C3 ⋊ C2 |
| Hall | C43×D29 ⋊ C3 |
| Sylow | C43 ⋊ C3×D29 |
| Sylow | C29 ⋊ C2×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C43 | C2×C3 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | (C43⋊C3)⋊#1181, #1181×C43⋊C3, D29×D43⋊C3, … |
| maximal normal subgroup of | (C43⋊C3)⋊#1181, #1181×C43⋊C3, D29×D43⋊C3, … |
| maximal quotient of | Dic29×C43⋊C3, C2×D29×C43⋊C3, D29×C43⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7482, 11);