Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C4⋊(C3⋊((C24⋊C5)⋊C2)) |
| Fitting | C24×C3×C4 ⋊ D5 |
| Sylow | C3 ⋊ C4⋊((C24⋊C5)⋊C2) |
716 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 716 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:
2^3,3,5,2^4|b^2=c,b^a=bc,d^a=d^2,e^a=e^4,f^a=fgi,h^a=hi,f^e=g,g^e=fgi,h^e=fh,i^e=fghi60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240267);