Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1485 |
218 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^52,c^b=cfg,d^b=df766 conjugacy classes — view the full character table.
| maximal subgroup of | #27275952, #27275953, #27275966, … |
| maximal normal subgroup of | #27275952, #27275953, #27275966, … |
| maximal quotient of | #27272521, #27272544, #27272553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2931);