Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#11719924 |
| Fitting | C8×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27295855, C16×#11719924, #27295862, … |
| maximal normal subgroup of | #27295855, C16×#11719924, #27295862, … |
| maximal quotient of | C8×#13133137, C8×#13133141, C8×#13133148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3310);