Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | Q8⋊C8×D53 |
| Fitting | C53×Q8⋊C8 ⋊ C2 |
| Sylow | C53 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊C8×D53, D53×#1476, D53×#1479, … |
| maximal normal subgroup of | C2×Q8⋊C8×D53, D53×#1476, D53×#1479, … |
| maximal quotient of | D53×#1271, D53×#1272, #27272036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2885);