Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #427×D53 |
| Fitting | C53×#427 ⋊ C2 |
| Sylow | C53 ⋊ C2×#427 |
512 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1382, #27298987, D53×#1384, … |
| maximal normal subgroup of | D53×#1382, #27298987, D53×#1384, … |
| maximal quotient of | D53×#1564, D53×#1568, #27353101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13086);