Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#341 ⋊ C2 |
| Sylow | C53 ⋊ #2019 |
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|a^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^52,c^b=cf,d^b=dg,f^b=fg,h^b=h^52,d^c=dg,e^c=eg,f^c=fg,h^c=h^52754 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2019, C2×#20275832, #27411296, … |
| maximal normal subgroup of | D53×#2019, C2×#20275832, #27411296, … |
| maximal quotient of | #27284700, #27284717, #27284768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5627);