Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | AGL(1,𝔽16)⋊Q8 |
| unambiguous semidirect product | ((C24⋊C5)⋊Q8)⋊C3 |
| Hall | (C24⋊C5)⋊Q8 ⋊ C3 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^2,3,2,5,2^4|a^2=d,b^2=d,b^a=bd,e^a=e^4,f^a=fgh,g^a=gi,h^a=hi,f^c=fhi,g^c=fi,h^c=fgh,i^c=gh,f^e=g,g^e=gi,h^e=gh,i^e=fhi44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239968);