Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×C22⋊D53 |
| Fitting | C22×D8×C53 ⋊ C2 |
| Sylow | C53 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
763 conjugacy classes — view the full character table.
| maximal subgroup of | #27540544, #27540548, #27540550, … |
| maximal normal subgroup of | #27540544, #27540548, #27540550, … |
| maximal quotient of | #27373435, #27373440, #27373450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16181);