Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #473 |
| Sylow | C5 ⋊ #4755 |
| Sylow | C3 ⋊ #65044 |
200 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=f,c^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^4,c^b=ce,d^b=df,g^b=g^2,e^c=ef69 conjugacy classes — view the full character table.
| maximal subgroup of | #14429452, C2×#11748201, D5×#4755, … |
| maximal normal subgroup of | #14429452, C2×#11748201, D5×#4755, … |
| maximal quotient of | #14291518, #14291557, #14291722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2396);