Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(((C24⋊C5)⋊C2)⋊C3) |
| unambiguous semidirect product | (C4⋊((C24⋊C5)⋊C2))⋊C3 |
| Fitting | C24×C4 ⋊ C3×D5 |
| Hall | C4⋊((C24⋊C5)⋊C2) ⋊ C3 |
186 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^2,3,2,5,2^4|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, 239970);