Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#13133249 |
| Fitting | C4×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
772 conjugacy classes — view the full character table.
| maximal subgroup of | #27353514, C8×#13133249, #27353536, … |
| maximal normal subgroup of | #27353514, C8×#13133249, #27353536, … |
| maximal quotient of | C8×#13133249, #27353687, #27353707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13330);