Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16810361 |
| Sylow | C53 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27274970, C4×#16810361, #27274980, … |
| maximal normal subgroup of | #27274970, C4×#16810361, #27274980, … |
| maximal quotient of | C2×#20272539, C2×#20272540, #27272057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2992);