Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #418 |
| Sylow | C5 ⋊ #5001 |
| Sylow | C3 ⋊ #65059 |
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=d,e^2=f,c^a=cf,h^a=h^4,c^b=ce,e^b=ef,g^b=g^2,e^c=ef90 conjugacy classes — view the full character table.
| maximal subgroup of | #14412389, D3×#65059, D5×#5001, … |
| maximal normal subgroup of | #14412389, D3×#65059, D5×#5001, … |
| maximal quotient of | #14281698, #14281996, #14282294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1670);