Finite Group DatabasebetaFinite Group Databasebeta| order | 5409 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C601⋊C3 |
| unambiguous semidirect product | C601⋊C32 |
| unambiguous semidirect product | (C3×C601)⋊C3 |
| Fitting, socle | C3×C601 ⋊ C3 |
| derived, Sylow | C601 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C601⋊C3 |
| commutator, hypocenter | C601 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C601 | C3 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
609 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D601⋊C3, C3⋊(D601⋊C3), D3×C601⋊C3, … |
| maximal normal subgroup of | C3×D601⋊C3, C3⋊(D601⋊C3), D3×C601⋊C3, … |
| maximal quotient of | C2×C3×C601⋊C3, C9×C601⋊C3, C3×C601⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5409, 3);