Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C5 ⋊ D16 |
| Sylow | C32 ⋊ #3958 |
| Sylow | C5 ⋊ #63734 |
100 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=f^2g,h^a=h^4,c^b=cd,d^b=de,f^b=f^2g^2,f^c=f^2,g^c=g^263 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1903);