Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #67180⋊C3 |
| Hall | C5×H(3,𝔽3) ⋊ Q8 |
| Sylow | H(3,𝔽3) ⋊ Dic10 |
| Sylow | C5 ⋊ #634⋊C3 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^2,3,2,3^2,5|a^2=d,b^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^4,e^c=ef119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 209);