Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C71 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D3×C71 |
| unambiguous semidirect product | C3⋊(C2×C3×C5×C71) |
| Fitting, socle, Hall | C32×C5×C71 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C5×C71 |
| Hall | C32×C71 ⋊ C2×C5 |
| Hall | C32×C5 ⋊ C2×C71 |
| Sylow | C32 ⋊ C2×C5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C71 | D3 |
| commutator, hypocenter | C3 | C2×C3×C5×C71 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C71 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C5×C71 | |
36 conjugacy classes of subgroups.
3195 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D3×D71, C3×D3×D5×C71, C3×D3×D355, … |
| maximal normal subgroup of | C3×C5×D3×D71, C3×D3×D5×C71, C3×D3×D355, … |
| maximal quotient of | C3×C5×Dic3×C71, C2×C3×C5×D3×C71, C3×D3×C25×C71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 23);