Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×SD16×D53 |
| Fitting | C4×SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | C8×SD16×D53, D53×SD16⋊C8, #27353552, … |
| maximal normal subgroup of | C8×SD16×D53, D53×SD16⋊C8, #27353552, … |
| maximal quotient of | C8×SD16×D53, D53×#1583, D53×#1582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13263);