Finite Group DatabasebetaFinite Group Databasebeta| order | 7404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D617 |
| unambiguous semidirect product | (D3×C617)⋊C2 |
| unambiguous semidirect product | (C3×D617)⋊C2 |
| unambiguous semidirect product | D1851⋊C2 |
| Fitting, socle, derived, Hall | C3×C617 ⋊ C22 |
| Sylow | C617 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D617 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C617 | C22 |
| LCS | G ▷ C3×C617 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
930 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D617, C3×D3×D617, D3×D1851, … |
| maximal normal subgroup of | C3×D3×D617, C5×D3×D617 |
| maximal quotient of | D9×D617, C3×D3×D617, D3×D1851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7404, 8);