Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #611⋊AGL(1,𝔽5) |
| Fitting | C22×C5×C9 ⋊ C2×C4 |
| Hall | C5×C9 ⋊ C4×D4 |
| Sylow | C9 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #611⋊C4 |
282 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^5,3,5,3|a^2=d,f^3=h,c^a=ce,g^a=g^2,c^b=ce,f^b=f^2h^2,h^b=h^2,g^d=g^481 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D9×AGL(1,𝔽5), #72247459, #72247590, … |
| maximal normal subgroup of | D4×D9×AGL(1,𝔽5), #72247459 |
| maximal quotient of | #72247590, #72247599 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1508);