Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(1,𝔽16)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#10623980 |
| derived, Hall | C32×C5 ⋊ C22×C8 |
| Sylow | C32 ⋊ C22×#170 |
| Sylow | C5 ⋊ C2×#3710 |
358 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5055);