Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66146⋊C3 |
| Hall | #66146 ⋊ C3 |
| Sylow | C5 ⋊ #519⋊C3 |
172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^2,3,2^3,5,2|a^2=d,e^2=h,f^2=h,b^a=bh,g^a=g^4,e^c=f,f^c=efh,f^e=fh94 conjugacy classes — view the full character table.
| maximal subgroup of | #14511797, #14511798, #10614287⋊C3, … |
| maximal normal subgroup of | #14511797, #14511798, #10614287⋊C3, … |
| maximal quotient of | #10614166⋊C3, #10614168⋊C3, #10614181⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6388);