Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14519842 |
| Fitting | C4×Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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 | C8×#14519842, #30597624, #30597628, … |
| maximal normal subgroup of | C8×#14519842, #30597624, #30597628, … |
| maximal quotient of | C4×#16840610, C4×Q8⋊#92420, #30597556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20271);