Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #465 |
| Sylow | C5 ⋊ #5171 |
| Sylow | C3 ⋊ #65330 |
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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=be,c^a=cd,d^a=df,h^a=h^4,c^b=ce,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5171, D3×#65330, C2×#11749050, … |
| maximal normal subgroup of | D5×#5171, D3×#65330, C2×#11749050, … |
| maximal quotient of | #14291300, #14291363, #14291582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3245);