Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C13×C13⋊C3 |
| unambiguous semidirect product | (C2×C13)⋊(C3×C5×C13) |
| unambiguous semidirect product | (C2×C5×C13)⋊(C3×C13) |
| Fitting, socle, Hall | C2×C5×C132 ⋊ C3 |
| derived | C13 ⋊ C2×C3×C5×C13 |
| Hall | C5×C132 ⋊ C2×C3 |
| Hall | C2×C132 ⋊ C3×C5 |
| Sylow | C132 ⋊ C2×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C13 | C13⋊C3 |
| commutator, hypocenter | C13 | C2×C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C132 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C5×C13 | |
48 conjugacy classes of subgroups.
910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 33);