Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D13×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C32×D13) |
| Fitting, socle | C3×C132 ⋊ C22×C3 |
| derived, Sylow | C132 ⋊ C22×C32 |
| Hall | C3×C13×C13⋊C3 ⋊ C22 |
| Hall | D132 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D13×D13⋊C3 |
| commutator, hypocenter | C132 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×D13×D13⋊C3, C3×D13×C5⋊(D13⋊C3), C3×D13⋊C3×D65, … |
| maximal normal subgroup of | C3×C5×D13×D13⋊C3 |
| maximal quotient of | C3×C5×D13×D13⋊C3, C3×D13×C5⋊(D13⋊C3), C3×D13⋊C3×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 187);