Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1588 |
166 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 54 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,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^30,d^b=df,h^b=h^52,h^c=h^30,h^e=h^52220 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20290343, D53⋊#1588, #28316484, … |
| maximal normal subgroup of | C2×#20290343, D53⋊#1588, #28316484, … |
| maximal quotient of | #28301776, #28301803, #28302148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20138);