Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16811433 |
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #27400004, #27400028, #27400080, … |
| maximal normal subgroup of | #27400004, #27400028, #27400080, … |
| maximal quotient of | C2×#20283240, C2×#20283246, C2×#20283309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19269);