Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#469 ⋊ C2 |
| Sylow | C53 ⋊ #2190 |
226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,e^b=eg,f^b=fg,h^b=h^52,d^c=dg436 conjugacy classes — view the full character table.
| maximal subgroup of | #27296257, #27296258, #27296268, … |
| maximal normal subgroup of | #27296257, #27296258, #27296268, … |
| maximal quotient of | #27296188, #27296193, #27296198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6455);