Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C71⋊C5 |
| unambiguous semidirect product | C3⋊(C2×C3×C71⋊C5) |
| unambiguous semidirect product | (D3×C71)⋊(C3×C5) |
| unambiguous semidirect product | (C3×D3×C71)⋊C5 |
| Fitting, socle, Hall | C32×C71 ⋊ C2×C5 |
| derived | C3×C71 ⋊ C2×C3×C5 |
| Hall | C32×C71⋊C5 ⋊ C2 |
| Hall | C3×D3×C71 ⋊ C5 |
| Sylow | C71 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ C2×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C71⋊C5 |
| commutator, hypocenter | C3×C71 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C71 | C2×C5 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×D71⋊C5, D3×C3⋊(D71⋊C5), D32×C71⋊C5, … |
| maximal normal subgroup of | C3×D3×D71⋊C5, D3×C3⋊(D71⋊C5), D32×C71⋊C5, … |
| maximal quotient of | C3×Dic3×C71⋊C5, C2×C3×D3×C71⋊C5, C3×D3×C71⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 16);