Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic130⋊C3 |
| Hall | Dic130 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ Q8 |
| Hall | C5×C13 ⋊ C3×Q8 |
| Hall | C13⋊C3 ⋊ Dic10 |
| Sylow | C13 ⋊ C3×Dic10 |
| Sylow | C5 ⋊ (C13⋊C3)⋊Q8 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 520 |
Polycyclic presentation:
2^2,3,2,5,13|a^2=d,b^2=d,b^a=bd,e^a=e^4,f^a=f^12,f^c=f^379 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 37);