Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D132 |
| Fitting, Hall | C9×C132 ⋊ C22 |
| derived, Sylow | C132 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D132 |
| commutator, hypocenter | C132 | C22×C9 |
| Frattini | C3 | C3×D132 |
| Fitting | C9×C132 | C22 |
| socle | C3×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C9 | |
96 conjugacy classes of subgroups.
576 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×D132, C9×D13×D65, C9×D65⋊D13 |
| maximal normal subgroup of | C5×C9×D132 |
| maximal quotient of | C5×C9×D132, C9×D13×D65, C9×D65⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 105);