Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#137×D53 |
| Fitting | C2×#137×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#137 |
1464 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1882, #27385612, D53×#1902, … |
| maximal normal subgroup of | D53×#1882, #27385612, D53×#1902, … |
| maximal quotient of | C2×#419×D53, C2×#417×D53, C2×#428×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19246);