Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D65 |
| unambiguous semidirect product | C5⋊(D13×C13⋊C3) |
| Fitting, socle, derived, Hall | C5×C132 ⋊ C2×C3 |
| Hall | C5×C13×C13⋊C3 ⋊ C2 |
| Hall | C13×D65 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ D5 |
| Sylow | C132 ⋊ C3×D5 |
| Sylow | C5 ⋊ D13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 31);