Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic90⋊C3 |
| Hall | C5×3−1+2 ⋊ Q8 |
| Sylow | 3−1+2 ⋊ Dic10 |
| Sylow | C5 ⋊ 3−1+2⋊Q8 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^2,3,2,3,5,3|a^2=d,b^2=d,e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^4,g^a=g^2,e^c=eg^2119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 212);