Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊(A4⋊AGL(1,𝔽5)) |
| Fitting | C22×C4×C5 ⋊ Dic3 |
| Sylow | C5 ⋊ C4⋊SL(2,ℤ/4) |
218 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 36 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:
2^4,3,5,2^2|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^3,g^a=h,h^a=g,f^c=f^4,g^e=h,h^e=gh44 conjugacy classes — view the full character table.
| maximal subgroup of | #14512357, #14512358, #14512363, … |
| maximal normal subgroup of | #14512357, #14512358, #14512363, … |
| maximal quotient of | C4⋊#91885, #14512446, C4⋊#91886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10913);