Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D5×C169⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C169⋊C3) |
| unambiguous semidirect product | (D5×C169)⋊C3 |
| Fitting, derived, Hall | C5×C169 ⋊ C2×C3 |
| Hall | C5×C169⋊C3 ⋊ C2 |
| Hall | D5×C169 ⋊ C3 |
| Sylow | C169 ⋊ C3×D5 |
| Sylow | C5 ⋊ C2×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C169 | C2×C3 |
| Frattini | C13 | D5×C13⋊C3 |
| socle | C5×C13 | C2×C13⋊C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
236 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×C169⋊C3, D15×C169⋊C3, D25×C169⋊C3, … |
| maximal normal subgroup of | C3×D5×C169⋊C3, C5×D5×C169⋊C3, C7×D5×C169⋊C3 |
| maximal quotient of | D5×C169⋊C9, C3×D5×C169⋊C3, D15×C169⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 3);