Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×#170 |
| Hall | C3×C5 ⋊ C8×D4 |
| Sylow | C5 ⋊ C3×C8×D4 |
268 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10603935, C3×D8×#170, #14286110, … |
| maximal normal subgroup of | C3×#10603935, C3×D8×#170, #14286110, … |
| maximal quotient of | C3×D8×#170, C3×SD16×#170, C3×Q16×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6500);