Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×C5×#886 |
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#123 |
| Sylow | C3 ⋊ C2×C5×#123 |
684 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 684 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 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68963, #14301694, C5×#68954, … |
| maximal normal subgroup of | C5×#68963, #14301694, C5×#68954, … |
| maximal quotient of | C2×C5×#4943, C2×C5×#4950, C2×C5×#4958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10072);