Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D8×D53 |
| Fitting | C4×D8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1331, #27293839, D53×#1333, … |
| maximal normal subgroup of | D53×#1331, #27293839, D53×#1333, … |
| maximal quotient of | C8×D8×D53, D53×#1581, D53×#1589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13257);