Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1885 |
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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.
Polycyclic presentation:
2^7,53|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^52,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg916 conjugacy classes — view the full character table.
| maximal subgroup of | #27299901, #27299906, #27299915, … |
| maximal normal subgroup of | #27299901, #27299906, #27299915, … |
| maximal quotient of | #27278737, #27278757, #27279007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4898);