Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C9×C13×#261 |
| Fitting, Hall | C9×C132 ⋊ C4 |
| derived | C13 ⋊ C4×C9×C13 |
| Sylow | C132 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C13 | #261 |
| commutator, hypocenter | C13 | C4×C9×C13 |
| Frattini | C3 | C3×C13×#261 |
| Fitting | C9×C132 | C4 |
| socle | C3×C132 | C3×C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C9×C13 | |
45 conjugacy classes of subgroups.
819 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×C13×#261, C9×C13×#63122, C9×C13×#63121, … |
| maximal normal subgroup of | C5×C9×C13×#261 |
| maximal quotient of | C5×C9×C13×#261, C9×C13×#63122, C9×C13×#63121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 101);