Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#3667 |
| Hall | C5×C9 ⋊ C2×M16 |
| Sylow | C9 ⋊ D5⋊M16 |
| Sylow | C5 ⋊ C2×#3667 |
204 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^5,3,5,3|a^2=d,b^2=e,d^2=e,f^3=h,c^a=ce,f^a=f^2h^2,g^a=g^2,h^a=h^2,g^d=g^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1558);