Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16840614 |
| Fitting | C2×C4⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
338 conjugacy classes — view the full character table.
| maximal subgroup of | #30597732, C4×#16840614, #30597742, … |
| maximal normal subgroup of | #30597732, C4×#16840614, #30597742, … |
| maximal quotient of | C2×#21460636, C2×#21460637, #30595351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19877);