Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD32×#6923 |
| Fitting | SD32×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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 | C2×SD32×#6923, #508×#6923, #509×#6923, … |
| maximal normal subgroup of | C2×SD32×#6923, #508×#6923, #509×#6923, … |
| maximal quotient of | SD32×#92420, #30605889, #30605890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20904);