Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C13×C13⋊C3 |
| unambiguous semidirect product | (C22×C13⋊C3)⋊(C3×C13) |
| unambiguous semidirect product | (A4×C13)⋊(C3×C13) |
| unambiguous semidirect product | (C22⋊(C13⋊C3))⋊(C3×C13) |
| Fitting, socle, Hall | C22×C132 ⋊ C32 |
| derived | C22×C13 ⋊ C32×C13 |
| Sylow | C132 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | A4×C13⋊C3 |
| commutator, hypocenter | C22×C13 | C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C132 | C32 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C13 | |
76 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
| maximal subgroup of | C5×A4×C13×C13⋊C3, C13×C13⋊C3×A5 |
| maximal normal subgroup of | C5×A4×C13×C13⋊C3 |
| maximal quotient of | C5×A4×C13×C13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 224);