Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D355 |
| unambiguous semidirect product | C5⋊(C32×D71) |
| unambiguous semidirect product | C71⋊(C32×D5) |
| Fitting, socle, Hall | C32×C5×C71 ⋊ C2 |
| derived, Hall | C5×C71 ⋊ C2×C32 |
| Hall | C32×C71 ⋊ D5 |
| Sylow | C71 ⋊ C32×D5 |
| Hall | C32×C5 ⋊ D71 |
| Sylow | C5 ⋊ C32×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D355 |
| commutator, hypocenter | C5×C71 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C71 | C2 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
1611 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D71, C3×D3×D355, C3×D15⋊D71, … |
| maximal normal subgroup of | C32×D5×D71, C3×D3×D355, C3×D15⋊D71, … |
| maximal quotient of | C32×Dic355, C2×C32×D355, C32×D1775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 22);