Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q16×#92420 |
| Sylow | C61 ⋊ C8×Q16 |
164 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
266 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#92420, #30605890, Q32×#92420, … |
| maximal normal subgroup of | SD32×#92420, #30605890, Q32×#92420, … |
| maximal quotient of | #103×#92420, #107×#92420, #30599595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20096);