Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13133282 |
| Fitting | C22×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22×#104 |
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28306674, #28306676, #28307070, … |
| maximal normal subgroup of | #28306674, #28306676, #28307070, … |
| maximal quotient of | C22×#16811471, C22×Q8⋊#88324, C2×#20290009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21135);