Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×M16 ⋊ C4 |
| Hall | C3×C5 ⋊ #428 |
| Sylow | C5 ⋊ #5121 |
| Sylow | C3 ⋊ #65727 |
236 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 89 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,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^3,c^b=cf,h^d=h^472 conjugacy classes — view the full character table.
| maximal subgroup of | #14299582, #14299610, #14299627, … |
| maximal normal subgroup of | #14299582, #14299610, #14299627, … |
| maximal quotient of | #14285601, #14285603, #14285605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6581);