Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #102×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1934 |
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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=dfg,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^23,h^b=h^30,h^f=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20290805, #28320029, #28320033, … |
| maximal normal subgroup of | C2×#20290805, #28320029, #28320033, … |
| maximal quotient of | #28305488, #28305489, #28305490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20600);