Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C3⋊#11759816 |
| unambiguous semidirect product | (C2×C3)⋊#11759816 |
| Fitting, socle | C2×C3×C132 ⋊ C2×C3 |
| derived | C3×C132 ⋊ C22×C3 |
| Hall | C3×#92789 ⋊ C22 |
| Sylow | C132 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#11759816 |
| commutator, hypocenter | C3×C132 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C132 | C2×C3 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
186 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊#11759816, C2×C5×C3⋊#11759816, C2×C3⋊(C5⋊#11759816) |
| maximal normal subgroup of | C2×C5×C3⋊#11759816 |
| maximal quotient of | D5×C3⋊#11759816, C2×C5×C3⋊#11759816, C2×C3⋊(C5⋊#11759816) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 241);