Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#16840709 |
| unambiguous semidirect product | D61⋊#385 |
| Fitting | C2×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#385 |
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
356 conjugacy classes — view the full character table.
| maximal subgroup of | #30602963, #30602978, #30603285, … |
| maximal normal subgroup of | #30602963, #30602978, #30603285, … |
| maximal quotient of | C2×#21460992, C2×#21460999, C4×#16840709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20960);