Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810585 |
| Fitting | C2×C22⋊C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#407 |
1008 conjugacy classes of subgroups.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27273690, #27273696, #27273702, … |
| maximal normal subgroup of | #27273690, #27273696, #27273702, … |
| maximal quotient of | C2×#20273040, C2×#20273043, C2×#20273046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12944);