Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810404 |
| Fitting | C2×M32×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299131, C4×#16810404, #27299135, … |
| maximal normal subgroup of | #27299131, C4×#16810404, #27299135, … |
| maximal quotient of | C2×#20272638, #27293153, C2×#20272654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6127);