Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Fitting | C32×C42×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ #117 |
| Sylow | C32 ⋊ #4018 |
| Sylow | C5 ⋊ #64081 |
456 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|b^2=e,c^2=d,c^a=ce,f^a=f^2,g^a=g^2,h^a=h^4372 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4458);