Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #4380⋊Q8 |
| Hall | C32×C5 ⋊ C4×Q8 |
| Sylow | C32 ⋊ Q8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Q8×#157 |
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=d,b^2=e,c^2=e,f^a=fg,g^a=fg^2,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^2,f^d=f^2,g^d=g^2,h^d=h^451 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5064);