Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13133280 |
| unambiguous semidirect product | D53⋊(C2×#103) |
| Fitting | C22×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22×#103 |
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28306670, #28306671, #28307077, … |
| maximal normal subgroup of | #28306670, #28306671, #28307077, … |
| maximal quotient of | C22×Q8⋊#88324, C2×D53⋊(Q8⋊C8), C22×#16811473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21125);