Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×SD16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1973 |
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 78 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=f,b^2=df,c^2=eg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^23,c^b=cg,h^b=h^30,h^f=h^52214 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20290865, #28320358, #28320360, … |
| maximal normal subgroup of | C2×#20290865, #28320358, #28320360, … |
| maximal quotient of | #28305760, #28305761, #28305762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20660);