Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
| direct product | D5×#92789 |
| unambiguous semidirect product | C5⋊(C2×#92789) |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C2×C3 |
| Hall | C5×#92789 ⋊ C2 |
| Hall | D5×C132 ⋊ C3 |
| Sylow | C132 ⋊ C3×D5 |
| Sylow | C5 ⋊ C2×#92789 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
236 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C13⋊C32, C3×D5×#92789, D15×#92789, … |
| maximal normal subgroup of | D5×C13⋊C32, C3×D5×#92789, C5×D5×#92789, … |
| maximal quotient of | D5×#13095201, C3×D5×#92789, D15×#92789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 30);