Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #423 |
| Sylow | C5 ⋊ #5118 |
| Sylow | C3 ⋊ #65682 |
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cf,h^a=h^2,g^b=g^2,h^d=h^472 conjugacy classes — view the full character table.
| maximal subgroup of | #14297856, #14297858, #14297864, … |
| maximal normal subgroup of | #14297856, #14297858, #14297864, … |
| maximal quotient of | #14285674, #14285705, #14285750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6024);