Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810721 |
| Fitting | C2×C4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#440 |
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 | #27279500, #27279506, #27279522, … |
| maximal normal subgroup of | #27279500, #27279506, #27279522, … |
| maximal quotient of | C2×#20273525, C2×#20273570, C2×#20273593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13287);