Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811494 |
| Fitting | C2×C42×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#339 |
488 conjugacy classes of subgroups.
472 conjugacy classes — view the full character table.
| maximal subgroup of | #339×#6157, C4×#16811494, #28306378, … |
| maximal normal subgroup of | #339×#6157, C4×#16811494, #28306378, … |
| maximal quotient of | C2×#20289543, #28300140, #28300147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20187);