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 ⋊ #495 |
| Sylow | C5 ⋊ #5059 |
| Sylow | C3 ⋊ #65457 |
260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 260 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=e,c^2=f,d^2=f,b^a=bef,c^a=cef,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65457, D5×#5059, C2×#11749313, … |
| maximal normal subgroup of | D3×#65457, D5×#5059, C2×#11749313, … |
| maximal quotient of | #14293465, #14293489, #14293540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3508);