Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#806 |
| Fitting | C3×C5×C22⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#99 |
| Sylow | C5 ⋊ C2×#806 |
| Sylow | C3 ⋊ D5×#99 |
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #14295409, AGL(1,𝔽5)×#806, #14300350, … |
| maximal normal subgroup of | #14295409, AGL(1,𝔽5)×#806, #14300350, … |
| maximal quotient of | D5×#4468, D5×#4469, #14280863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1321);