Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#15690148 |
| derived, Sylow | C132 ⋊ C22×C9 |
| Hall | #13095200 ⋊ C22 |
| Hall | C2×C13⋊D13 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #11759815 |
| commutator, hypocenter | C132 | C22×C9 |
| Frattini | C3 | C2×#11759815 |
| Fitting, socle | C2×C3×C132 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C3 | |
240 conjugacy classes of subgroups.
204 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#15690148, C2×C5×#15690148, C2×C5⋊#15690148 |
| maximal normal subgroup of | C2×C5×#15690148 |
| maximal quotient of | D5×#15690148, C2×C5×#15690148, C2×C5⋊#15690148 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 94);