Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C3×Dic3×#170 |
| derived | C3×C5 ⋊ C3×C4×C8 |
| Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C4×#170 |
| Sylow | C5 ⋊ C3×C8×Dic3 |
198 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1718);