Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Dic3×SD16 |
| Hall | C3×C5 ⋊ C4×SD16 |
| Sylow | C3 ⋊ C4×C5×SD16 |
244 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C5×D3×SD16, C2×C5×Dic3×SD16, D5×Dic3×SD16, … |
| maximal normal subgroup of | C4×C5×D3×SD16, C2×C5×Dic3×SD16, D5×Dic3×SD16, … |
| maximal quotient of | C5×SD16×C3⋊C8, C5×#70895, C5×#70896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4855);