Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C3×#91164 |
| derived | C3×C5 ⋊ C2×C3×C16 |
| Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ D5⋊C16 |
| Sylow | C5 ⋊ C3×D3×C16 |
122 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 52 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, 1714);