Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of D5×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#10587069 |
| derived, Hall | C5×C13 ⋊ C2×C3×C4 |
| Hall | C3×C5×C13 ⋊ C2×C4 |
| Hall | C3×C13 ⋊ C4×D5 |
| Hall | C3×C5 ⋊ C4×D13 |
| Sylow | C13 ⋊ C3×C4×D5 |
| Sylow | C5 ⋊ C3×C4×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×D13 |
| commutator, hypocenter | C5×C13 | C2×C3×C4 |
| Frattini | C2 | C3×D5×D13 |
| Fitting, socle | C2×C3×C5×C13 | C22 |
| prime radical | C2×C3×D65 | C2 |
| cosocle | C2×C5×C13 | C22×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2×C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 780 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 56);