Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66262⋊C3 |
| Fitting | C2×C5×Q8 ⋊ C3×C4 |
| Hall | #66262 ⋊ C3 |
| Sylow | C5 ⋊ #519⋊C3 |
172 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^2,3,2^3,5,2|a^2=d,e^2=h,f^2=h,b^a=bh,g^a=g^2,e^c=ef,f^c=e,g^d=g^4,f^e=fh52 conjugacy classes — view the full character table.
| maximal subgroup of | #14512369, #14512370, #10617514⋊C3, … |
| maximal normal subgroup of | #14512369, #14512370, #10617514⋊C3, … |
| maximal quotient of | #10617199⋊C3, #10617202⋊C3, #10617208⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10932);