Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16811603 |
| Fitting | C22×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#410 |
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306521, #28306526, #28306551, … |
| maximal normal subgroup of | #28306521, #28306526, #28306551, … |
| maximal quotient of | C2×#20289947, C2×#20289955, C2×#20289959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21107);