Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #451 |
| Sylow | C5 ⋊ #5186 |
| Sylow | C3 ⋊ #65097 |
296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,h^a=h^4,c^b=cef,e^b=ef,g^b=g^2,e^c=ef81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5186, D3×#65097, #14423371, … |
| maximal normal subgroup of | D5×#5186, D3×#65097, #14423371, … |
| maximal quotient of | #14288018, #14288159, #14288582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3505);