Finite Group DatabasebetaFinite Group Databasebeta| order | 5070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×C3⋊(C13⋊D13) |
| unambiguous semidirect product | C3⋊(C5×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C5×D39) |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C2 |
| derived, Hall | C3×C132 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ D3 |
| Sylow | C132 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ C13⋊D13 |
| Sylow | C3 ⋊ C5×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(C13⋊D13) |
| commutator, hypocenter | C3×C132 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C2 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
1275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5070, 43);