Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | AΣL(1,𝔽16)×D61 |
| Fitting | C61×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C61 ⋊ 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.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AΣL(1,𝔽16)×D61, D61×#2120, D61×#2121, … |
| maximal normal subgroup of | C2×AΣL(1,𝔽16)×D61, D61×#2120, D61×#2121, … |
| maximal quotient of | D61×#1316, D61×#1326, #29589260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6140);