Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #5414 |
160 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 160 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) = 120 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^4,g^a=h,h^a=g,c^b=cd,g^e=h,h^e=gh59 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5414, #14513175, #14513178, … |
| maximal normal subgroup of | D5×#5414, #14513175, #14513178, … |
| maximal quotient of | #14511965, #14511966, #14512000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6328);