Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D11×AΣL(1,𝔽16) |
| Fitting | C11×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C11 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11×AΣL(1,𝔽16), D11×#2120, D11×#2121, … |
| maximal normal subgroup of | C2×D11×AΣL(1,𝔽16), D11×#2120, D11×#2121, … |
| maximal quotient of | D11×#1316, D11×#1326, #14663020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6140);