Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#16811524 |
| Fitting | C2×C22⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
286 conjugacy classes — view the full character table.
| maximal subgroup of | #28310577, C4×#16811524, #28310592, … |
| maximal normal subgroup of | #28310577, C4×#16811524, #28310592, … |
| maximal quotient of | C2×#20289640, C2×#20289659, #28308053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20757);