Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D53⋊#104 |
| unambiguous semidirect product | D53⋊(C2×#104) |
| Fitting | C2×#41×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22×#104 |
856 conjugacy classes of subgroups.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28306641, #28306642, #28306644, … |
| maximal normal subgroup of | #28306641, #28306642, #28306644, … |
| maximal quotient of | C2×D53⋊(D4⋊C8), C2×D53⋊(Q8⋊C8), C2×#20290006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21134);