Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(A4⋊Dic5) |
| Sylow | C5 ⋊ C4⋊SL(2,ℤ/4) |
218 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^4,g^a=h,h^a=g,g^e=h,h^e=gh92 conjugacy classes — view the full character table.
| maximal subgroup of | #14511758, #14511760, #14511771, … |
| maximal normal subgroup of | #14511758, #14511760, #14511771, … |
| maximal quotient of | C4⋊(A4⋊#168), C4⋊#91184, #14511978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6326);