Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#339 ⋊ C2 |
| Sylow | C53 ⋊ #2005 |
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=g,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^52,c^b=cf,d^b=dg,h^b=h^52,d^c=dg,h^c=h^52754 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2005, C2×#20275754, #27410996, … |
| maximal normal subgroup of | D53×#2005, C2×#20275754, #27410996, … |
| maximal quotient of | #27284312, #27284326, #27284368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5549);