Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#14519836 |
| Fitting | C23×C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
524 conjugacy classes — view the full character table.
| maximal subgroup of | #30602508, #30602510, #30602532, … |
| maximal normal subgroup of | #30602508, #30602510, #30602532, … |
| maximal quotient of | C22×#16840606, C22×#16840607, C2×#21461056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21104);