Finite Group DatabasebetaFinite Group Databasebeta| order | 6570 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C73 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D3×C73 |
| unambiguous semidirect product | C3⋊(C5×D3×C73) |
| Fitting, socle, Hall | C32×C5×C73 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C5×C73 |
| Hall | C32×C73 ⋊ C2×C5 |
| Hall | C32×C5 ⋊ C2×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C73 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C5×C73 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C73 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C73 | |
48 conjugacy classes of subgroups.
2190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C3⋊D3×D73, D5×C3⋊D3×C73, C3⋊D3×D365, … |
| maximal normal subgroup of | C5×C3⋊D3×D73, D5×C3⋊D3×C73, C3⋊D3×D365, … |
| maximal quotient of | C5×C3⋊Dic3×C73, C2×C5×C3⋊D3×C73, C3⋊D3×C25×C73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6570, 33);