Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×A4⋊#168 |
| unambiguous semidirect product | A4⋊(C3×#168) |
| derived | C5×A4 ⋊ C3×C8 |
| Sylow | C5 ⋊ C3×A4⋊C8 |
116 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 360 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2526);