Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q32×D53 |
| Fitting | C2×Q32×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×Q32 |
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1416, #27304537, D53×#1420, … |
| maximal normal subgroup of | D53×#1416, #27304537, D53×#1420, … |
| maximal quotient of | C2×#358×D53, C2×#366×D53, C4×Q32×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17621);