Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | B(4,𝔽2)×D53 |
| Fitting | C53×B(4,𝔽2) ⋊ C2 |
| Sylow | C53 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
448 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2196, D53×#2197, D53×#2199, … |
| maximal normal subgroup of | D53×#2196, D53×#2197, D53×#2199, … |
| maximal quotient of | D53×#1595, D53×#1601, D53×#1596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13892);