Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×(C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic5×(C22⋊C9)⋊C2 |
| derived | C5×C22⋊C9 ⋊ C2×C4 |
| Sylow | C5 ⋊ C4×(C22⋊C9)⋊C2 |
192 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1472);