Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #501 |
| Sylow | C5 ⋊ #4876 |
| Sylow | C3 ⋊ #65354 |
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 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=d,c^2=d,e^2=f,b^a=bf,c^a=ce,h^a=h^4,c^b=cdf,g^b=g^2,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65354, D5×#4876, #14439919, … |
| maximal normal subgroup of | D3×#65354, D5×#4876, #14439919, … |
| maximal quotient of | #14299168, #14305159, #14305160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1356);