Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810745 |
| Sylow | C53 ⋊ C2×#444 |
464 conjugacy classes of subgroups.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27299386, #27299388, #27299393, … |
| maximal normal subgroup of | #27299386, #27299388, #27299393, … |
| maximal quotient of | C2×SD16⋊#88322, C2×#20273534, C2×#20273539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13406);