Finite Group DatabasebetaFinite Group Databasebeta| order | 6570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1095 |
| unambiguous semidirect product | C5⋊(C3⋊D219) |
| unambiguous semidirect product | C73⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C5×C73 ⋊ C2 |
| Hall | C32×C73 ⋊ D5 |
| Hall | C5×C73 ⋊ C3⋊D3 |
| Sylow | C73 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D73 |
| Sylow | C32 ⋊ D365 |
| Sylow | C5 ⋊ C3⋊D219 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C73 | C2 |
| LCS | G ▷ C32×C5×C73 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,73|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^721644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D15×D73, D5×C3⋊D219, C3⋊D3×D365, … |
| maximal normal subgroup of | C3⋊D15×D73, D5×C3⋊D219, C3⋊D3×D365, … |
| maximal quotient of | C3⋊Dic1095, C2×C3⋊D1095, C3⋊D5475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6570, 36);