Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#91774 |
| Fitting | C32×C5×C22⋊C4 ⋊ C2 |
| Hall | C32×C5 ⋊ #124 |
| Sylow | C32 ⋊ #4031 |
| Sylow | C5 ⋊ C3×#885 |
338 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4293);