Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C9×C71⋊C5 |
| unambiguous semidirect product | (C2×C71)⋊(C5×C9) |
| unambiguous semidirect product | (C2×C9×C71)⋊C5 |
| Fitting, Hall | C2×C9×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C2×C5×C9 |
| Hall | C9×C71 ⋊ C2×C5 |
| Hall | C2×C71 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C71⋊C5 |
| commutator, hypocenter | C71 | C2×C5×C9 |
| Frattini | C3 | C2×C3×C71⋊C5 |
| Fitting | C2×C9×C71 | C5 |
| socle | C2×C3×C71 | C3×C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C9 | |
24 conjugacy classes of subgroups.
342 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C9×C71⋊C5, C9×Dic71⋊C5, Dic9×C71⋊C5, … |
| maximal normal subgroup of | C4×C9×C71⋊C5, C9×Dic71⋊C5, Dic9×C71⋊C5, … |
| maximal quotient of | C4×C9×C71⋊C5, C22×C9×C71⋊C5, C2×C9×C71⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 2);