Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16810595 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#410 |
788 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | #27299033, #27299041, #27299060, … |
| maximal normal subgroup of | #27299033, #27299041, #27299060, … |
| maximal quotient of | C2×#20273026, C2×#20273028, C2×#20273034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12965);