Finite Group DatabasebetaFinite Group Databasebeta| order | 6054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1009 |
| Fitting, socle, Hall | C3×C1009 ⋊ C2 |
| derived, Sylow | C1009 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1009 |
| commutator, hypocenter | C1009 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1009 | C2 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
1518 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#16860937, C3⋊#16860937, D3×D1009, … |
| maximal normal subgroup of | C3×#16860937, C3⋊#16860937, D3×D1009, … |
| maximal quotient of | C3×Dic1009, C2×C3×D1009, C9×D1009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6054, 4);