Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q8⋊C8 |
| Sylow | C5 ⋊ #4535 |
| Sylow | C3 ⋊ #64676 |
140 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 140 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) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=e,b^2=cd,c^2=e,d^2=f,b^a=bc,c^a=ce,h^a=h^4,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #14281530, D5×#4535, C2×#11745841, … |
| maximal normal subgroup of | #14281530, D5×#4535, C2×#11745841, … |
| maximal quotient of | #14276669, #14276684, #14276805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 36);