Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×#11759816 |
| Fitting, socle, Hall | C5×C132 ⋊ C2×C3 |
| derived, Sylow | C132 ⋊ C2×C3×C5 |
| Hall | C5×#92789 ⋊ C2 |
| Hall | C5×C13⋊D13 ⋊ C3 |
| Hall | #92789 ⋊ C2×C5 |
| Hall | C13⋊D13 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11759816 |
| commutator, hypocenter | C132 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 16);