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 ⋊ #65407 |
252 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 111 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=e,c^2=d,d^2=f,c^a=ce,g^a=g^2,h^a=h^4,c^b=cf168 conjugacy classes — view the full character table.
| maximal subgroup of | #14277721, #14277730, #14297555, … |
| maximal normal subgroup of | #14277721, #14277730, #14297555, … |
| maximal quotient of | #14285649, #14285680, #14285711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5414);