Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D845 |
| unambiguous semidirect product | C5⋊(C3×D169) |
| Fitting, Hall | C3×C5×C169 ⋊ C2 |
| derived, Hall | C5×C169 ⋊ C2×C3 |
| Hall | C3×C169 ⋊ D5 |
| Sylow | C169 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ D169 |
| Sylow | C5 ⋊ C3×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D845 |
| commutator, hypocenter | C5×C169 | C2×C3 |
| Frattini | C13 | C3×D65 |
| Fitting | C3×C5×C169 | C2 |
| socle | C3×C5×C13 | D13 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
1272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊(D169⋊C9), C9×D845, C3×C5⋊(D169⋊C3), … |
| maximal normal subgroup of | C5⋊(D169⋊C9), C9×D845, C3×C5⋊(D169⋊C3), … |
| maximal quotient of | C9×D845, C32×D845, C3×D2535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 8);