Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1065 |
| unambiguous semidirect product | C3⋊(C3×D355) |
| unambiguous semidirect product | C5⋊(C3×D213) |
| unambiguous semidirect product | C71⋊(C3×D15) |
| Fitting, socle, Hall | C32×C5×C71 ⋊ C2 |
| derived | C3×C5×C71 ⋊ C2×C3 |
| Hall | C32×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ C3×D3 |
| Sylow | C71 ⋊ C3×D15 |
| Hall | C32×C5 ⋊ D71 |
| Sylow | C32 ⋊ D355 |
| Sylow | C5 ⋊ C3×D213 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1065 |
| commutator, hypocenter | C3×C5×C71 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C71 | C2 |
| LCS | G ▷ C3×C5×C71 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
1602 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D15×D71, C3×D5×D213, C3×D3×D355, … |
| maximal normal subgroup of | C3×D15×D71, C3×D5×D213, C3×D3×D355, … |
| maximal quotient of | C3×Dic1065, C2×C3×D1065, C3×D5325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 26);