Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C5 ⋊ SD32 |
| Sylow | C32 ⋊ #3959 |
| Sylow | C5 ⋊ #63549 |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,h^a=h^4,c^b=cd,d^b=de,f^b=f^2,g^b=g^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1198);