Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C9×C22⋊C4 ⋊ C2 |
| Hall | C5×C9 ⋊ #99 |
| Sylow | C9 ⋊ #3938 |
| Sylow | C5 ⋊ #63365 |
156 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 156 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.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^5,3,5,3|b^2=c,f^3=h,b^a=bd,c^a=ce,f^a=f^2h^2,g^a=g^4,h^a=h^2,d^b=de231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 166);