Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #453 |
| Sylow | C5 ⋊ #4822 |
| Sylow | C3 ⋊ #65487 |
336 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=d,e^2=f,b^a=bd,c^a=ce,h^a=h^4,c^b=ce,e^b=ef,g^b=g^2,d^c=df,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65487, D5×#4822, #14424982, … |
| maximal normal subgroup of | D3×#65487, D5×#4822, #14424982, … |
| maximal quotient of | #14287694, #14287733, #14287922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3617);