Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3005 |
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27415445, #27415448, #27415482, … |
| maximal normal subgroup of | #27415445, #27415448, #27415482, … |
| maximal quotient of | #27356474, #27356513, #27356552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13749);