Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(C5⋊#857) |
| Fitting | C43×C5 ⋊ D3 |
| Sylow | C5 ⋊ C4⋊#857 |
328 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 27 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,f^2=h,g^2=i,b^a=bc,d^a=d^2,e^a=e^4,f^a=fg,g^a=gi,h^a=hi,f^d=ghi,g^d=fgh,h^d=i,i^d=hi92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237594);