Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^30,d^b=df,f^b=fg,h^c=h^30,h^e=h^52187 conjugacy classes — view the full character table.
| maximal subgroup of | #28312649, #28312650, #28312652, … |
| maximal normal subgroup of | #28312649, #28312650, #28312652, … |
| maximal quotient of | D16×#88324, #28309968, #28309973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20909);