Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#14523157 |
| Fitting, socle | C3×C132 ⋊ C3×C4 |
| derived, Sylow | C132 ⋊ C32×C4 |
| Hall | C3×C13×C13⋊C3 ⋊ C4 |
| Hall | #10621730 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14523157 |
| commutator, hypocenter | C132 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132 | C3×C4 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
74 conjugacy classes of subgroups.
111 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×#14523157, C3×#23778475, C3×#23778476, … |
| maximal normal subgroup of | C3×C5×#14523157 |
| maximal quotient of | C3×C5×#14523157, C3×#23778475, C3×#23778476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 186);