Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C3×C4×#168 |
| derived, Sylow | C5 ⋊ C2×C3×C4×C8 |
| Hall | C3×C5 ⋊ C2×C4×C8 |
324 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598144, #14276694, C3×#10598194, … |
| maximal normal subgroup of | C3×#10598144, #14276694, C3×#10598194, … |
| maximal quotient of | C2×C3×C8×#168, C2×C3×#64675, C3×M16×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4012);