Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #100×#6923 |
| Fitting | #100×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
209 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×#6923, #352×#6923, #30606511, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×#6923, #352×#6923, #30606511, … |
| maximal quotient of | #323×#6923, #30597457, #30597472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20261);