Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D213 |
| unambiguous semidirect product | C3⋊(C5×D213) |
| Fitting, socle, Hall | C32×C5×C71 ⋊ C2 |
| derived, Hall | C32×C71 ⋊ C2×C5 |
| Hall | C5×C71 ⋊ C3⋊D3 |
| Sylow | C71 ⋊ C5×C3⋊D3 |
| Hall | C32×C5 ⋊ D71 |
| Sylow | C32 ⋊ C5×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D213 |
| commutator, hypocenter | C32×C71 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C71 | C2 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
1605 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C3⋊D3×D71, D5×C3⋊D213, D355⋊(C3⋊D3), … |
| maximal normal subgroup of | C5×C3⋊D3×D71, D5×C3⋊D213, D355⋊(C3⋊D3), … |
| maximal quotient of | C5×C3⋊Dic213, C2×C5×C3⋊D213, C25×C3⋊D213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 28);