Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×C4×#689 |
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ C3×C4×Q16 |
220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599006, C3×C8×#689, #14286245, … |
| maximal normal subgroup of | C3×#10599006, C3×C8×#689, #14286245, … |
| maximal quotient of | C3×C8×#689, C3×#10601749, C3×#10601727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4121);