Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810406 |
| Fitting | C22×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 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.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299139, C4×#16810406, #27299144, … |
| maximal normal subgroup of | #27299139, C4×#16810406, #27299144, … |
| maximal quotient of | C2×#20272640, #27293166, C2×#20272656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6133);