Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C3×#4082 |
| Hall | C3×C5 ⋊ C2×#124 |
| Sylow | C5 ⋊ C2×C3×#124 |
660 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10604936, #14281248, C2×C3×#64921, … |
| maximal normal subgroup of | C3×#10604936, #14281248, C2×C3×#64921, … |
| maximal quotient of | C2×C3×#65266, C2×C3×#65234, C2×C3×#65510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10003);