Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D45 |
| unambiguous semidirect product | C5⋊(D9×C71) |
| unambiguous semidirect product | C9⋊(D5×C71) |
| Fitting, Hall | C5×C9×C71 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C2×C71 |
| Hall | C9×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ D9 |
| Sylow | C9 ⋊ D5×C71 |
| Sylow | C5 ⋊ D9×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D45 |
| commutator, hypocenter | C5×C9 | C2×C71 |
| Frattini | C3 | D15×C71 |
| Fitting | C5×C9×C71 | C2 |
| socle | C3×C5×C71 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C71 | |
24 conjugacy classes of subgroups.
1704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×D71, D5×D9×C71, D45⋊D71, … |
| maximal normal subgroup of | D45×D71, D5×D9×C71, D45⋊D71, … |
| maximal quotient of | C71×Dic45, C2×C71×D45, C71×D225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 8);