Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ #330 |
| Sylow | C5 ⋊ #4543 |
| Sylow | C3 ⋊ #64685 |
120 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 46 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=f,b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,h^a=h^4,d^b=df,g^b=g^2105 conjugacy classes — view the full character table.
| maximal subgroup of | #14283897, D3×#64685, D5×#4543, … |
| maximal normal subgroup of | #14283897, D3×#64685, D5×#4543, … |
| maximal quotient of | #14276664, #14276669, #14277164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 44);