Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #5401 |
144 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=c,c^2=d,b^a=bcd,f^a=f^4,c^b=cd,e^b=e^2,g^b=h,h^b=g,g^e=h,h^e=gh50 conjugacy classes — view the full character table.
| maximal subgroup of | #14512903, D5×#5401, #14512912, … |
| maximal normal subgroup of | #14512903, D5×#5401, #14512912, … |
| maximal quotient of | #14511669, #14511671, #14511679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5768);