Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic3×#689 |
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ Dic3×Q16 |
| Sylow | C3 ⋊ C4×#689 |
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #14416157, D5×Dic3×Q16, C4×D3×#689, … |
| maximal normal subgroup of | #14416157, D5×Dic3×Q16, C4×D3×#689, … |
| maximal quotient of | C3⋊C8×#689, #14286812, #14286829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3450);