Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D169⋊C3 |
| unambiguous semidirect product | D169⋊(C3×C5) |
| unambiguous semidirect product | (C169⋊C3)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D169)⋊C3 |
| Fitting, Hall | C5×C169 ⋊ C2×C3 |
| derived, Sylow | C169 ⋊ C2×C3×C5 |
| Hall | C5×C169⋊C3 ⋊ C2 |
| Hall | C5×D169 ⋊ C3 |
| Hall | C169⋊C3 ⋊ C2×C5 |
| Hall | D169 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D169⋊C3 |
| commutator, hypocenter | C169 | C2×C3×C5 |
| Frattini | C13 | C5×D13⋊C3 |
| Fitting | C5×C169 | C2×C3 |
| socle | C5×C13 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
170 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×D169⋊C3, C5×C3⋊(D169⋊C3), C25×D169⋊C3, … |
| maximal normal subgroup of | C3×C5×D169⋊C3, C25×D169⋊C3, C52×D169⋊C3, … |
| maximal quotient of | C5×D169⋊C9, C3×C5×D169⋊C3, C5×C3⋊(D169⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 2);