Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#99×D53 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#99 |
1112 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1390, #27299037, D53×#1393, … |
| maximal normal subgroup of | D53×#1390, #27299037, D53×#1393, … |
| maximal quotient of | C2×#323×D53, C2×#324×D53, D53×#1459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12961);