Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #497 |
| Sylow | C5 ⋊ #4715 |
| Sylow | C3 ⋊ #65456 |
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 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=f,c^2=e,e^2=f,b^a=bd,c^a=cf,h^a=h^4,c^b=ce,e^b=ef,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65456, #14439034, D5×#4715, … |
| maximal normal subgroup of | D3×#65456, #14439034, D5×#4715, … |
| maximal quotient of | #14293675, #14293681, #14293773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2219);