Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×C3⋊#170 |
| derived, Hall | C32×C5 ⋊ C22×C8 |
| Sylow | C32 ⋊ C22×#170 |
| Sylow | C5 ⋊ C2×D3×C3⋊C8 |
326 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5028);