Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D9)⋊#170 |
| Hall | C5×C9 ⋊ C22⋊C8 |
| Sylow | C9 ⋊ C22⋊#170 |
| Sylow | C5 ⋊ (C2×D9)⋊C8 |
150 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3,5,3|a^2=c,c^2=e,f^3=h,b^a=bd,g^a=g^2,f^b=f^2h^2,h^b=h^2,g^c=g^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 249);