Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C13×C3⋊D3×D13 |
| unambiguous semidirect product | (C3×D13)⋊(D3×C13) |
| Fitting, socle, Hall | C32×C132 ⋊ C22 |
| derived | C32×C13 ⋊ C22×C13 |
| Sylow | C132 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊D3×D13 |
| commutator, hypocenter | C32×C13 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C132 | C22 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C13 | |
192 conjugacy classes of subgroups.
624 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C13×C3⋊D3×D13, C13×D13×C3⋊D15, C13×C3⋊D3×D65, … |
| maximal normal subgroup of | C5×C13×C3⋊D3×D13 |
| maximal quotient of | C5×C13×C3⋊D3×D13, C13×D13×C3⋊D15, C13×C3⋊D3×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 263);