Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#932 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C32 ⋊ C5×AGL(1,ℤ/8) |
326 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×#932, C5×#10595100, #72230423 |
| maximal normal subgroup of | C3×D5×#932, C5×#10595100, #72230423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4265);