Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16840150 |
| Fitting | C22×D8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C2×#496 |
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
872 conjugacy classes — view the full character table.
| maximal subgroup of | #29688550, C4×#16840150, #29688571, … |
| maximal normal subgroup of | #29688550, C4×#16840150, #29688571, … |
| maximal quotient of | C2×#21445440, C2×#21445442, C2×#21445445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14943);