Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #468 |
| Sylow | C5 ⋊ #5049 |
| Sylow | C3 ⋊ #65331 |
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,c^b=cef,d^b=df,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65331, #14427919, D5×#5049, … |
| maximal normal subgroup of | D3×#65331, #14427919, D5×#5049, … |
| maximal quotient of | #14292379, #14292442, #14292661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2743);