Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#16810811 |
| Fitting | C2×#99×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
604 conjugacy classes — view the full character table.
| maximal subgroup of | #27301351, #27301353, #27301365, … |
| maximal normal subgroup of | #27301351, #27301353, #27301365, … |
| maximal quotient of | C2×#20273634, C2×#20273635, C2×#20273668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13895);