Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #367×D53 |
| Fitting | C53×#367 ⋊ C2 |
| Sylow | C53 ⋊ C2×#367 |
168 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1418, D53×#1426, C2×#367×D53, … |
| maximal normal subgroup of | D53×#1418, D53×#1426, C2×#367×D53, … |
| maximal quotient of | D53×#1372, #27295735, #27295775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6288);