Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of #90866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×#90866 |
| Fitting, socle, Hall | C32×C132 ⋊ C4 |
| derived | C32×C13 ⋊ C4×C13 |
| Sylow | C132 ⋊ #157 |
| Sylow | C32 ⋊ C13×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #90866 |
| commutator, hypocenter | C32×C13 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C132 | C4 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C13 | |
58 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C13×#90866, C13×#14556842, C13×#14556843, … |
| maximal normal subgroup of | C5×C13×#90866 |
| maximal quotient of | C5×C13×#90866, C13×#14556842, C13×#14556843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 278);