Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#91236 |
| Fitting | C32×C5×D4 ⋊ C4 |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C32 ⋊ #4007 |
| Sylow | C5 ⋊ C3×#832 |
254 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#214, #72229595, C3×#11751944, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#214, #72229595, C3×#11751944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2602);