Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊#92788 |
| unambiguous semidirect product | (C22×C3)⋊#92788 |
| Fitting, socle | C22×C3×C132 ⋊ C3 |
| derived, Hall | C22×C132 ⋊ C32 |
| Sylow | C132 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊#92788 |
| commutator, hypocenter | C22×C132 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C132 | C3 |
| LCS | G ▷ C22×C132 | |
| UCS | C1 ◁ C3 | |
224 conjugacy classes of subgroups.
684 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×C22⋊#92788 |
| maximal normal subgroup of | C3×C5×C22⋊#92788 |
| maximal quotient of | C3×C5×C22⋊#92788 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 286);