Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #441 |
| Sylow | C5 ⋊ #5184 |
| Sylow | C3 ⋊ #65078 |
216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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=d,c^2=f,e^2=f,c^a=ce,e^a=ef,h^a=h^4,c^b=cef,e^b=ef,g^b=g^2,e^c=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65078, D5×#5184, #14416431, … |
| maximal normal subgroup of | D3×#65078, D5×#5184, #14416431, … |
| maximal quotient of | #14286399, #14287095, #14287116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3459);