Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1501 |
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 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,c^2=g,d^2=g,b^a=bd,d^a=df,h^a=h^52,d^b=dg,e^b=efg766 conjugacy classes — view the full character table.
| maximal subgroup of | #27275078, #27275081, #27275083, … |
| maximal normal subgroup of | #27275078, #27275081, #27275083, … |
| maximal quotient of | #27272044, #27272047, #27272051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3001);