Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#137×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2009 |
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,h^b=h^52,d^c=dg,e^c=eg595 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2009, C2×#20275773, #27411099, … |
| maximal normal subgroup of | D53×#2009, C2×#20275773, #27411099, … |
| maximal quotient of | #27284405, #27284419, #27284433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5568);