Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#13095200 |
| derived, Sylow | C132 ⋊ C22×C9 |
| Hall | C22×C132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #92788 |
| commutator, hypocenter | C132 | C22×C9 |
| Frattini | C3 | C22×#92788 |
| Fitting, socle | C22×C3×C132 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C22×C3 | |
240 conjugacy classes of subgroups.
708 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#13095200, C22×C5×#13095200 |
| maximal normal subgroup of | C22×C5×#13095200 |
| maximal quotient of | C2×D5×#13095200, C22×C5×#13095200 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 115);