Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#11759813 |
| Fitting, socle, Hall | C5×C132 ⋊ D3 |
| derived, Hall | #92789 ⋊ C2×C5 |
| Hall | C5×#92789 ⋊ C2 |
| Sylow | C132 ⋊ C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11759813 |
| commutator, hypocenter | #92789 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | D3 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C5 | |
30 conjugacy classes of subgroups.
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 21);