Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2177 |
172 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 48 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=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^23,d^b=df,f^b=fg,h^c=h^30,h^e=h^52175 conjugacy classes — view the full character table.
| maximal subgroup of | #28312659, #28312660, #28312661, … |
| maximal normal subgroup of | #28312659, #28312660, #28312661, … |
| maximal quotient of | #28309981, #28309982, #28309983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20908);