Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #103×#6923 |
| Fitting | #103×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C2×#103×#6923, #416×#6923, #419×#6923, … |
| maximal normal subgroup of | C2×#103×#6923, #416×#6923, #419×#6923, … |
| maximal quotient of | Q8⋊C8×#6923, #30597566, #30597569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20279);