Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#13133246 |
| Fitting | C4×SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
772 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13133246, #27353520, #27353534, … |
| maximal normal subgroup of | C8×#13133246, #27353520, #27353534, … |
| maximal quotient of | C8×#13133246, #27353681, #27353703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13324);