Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#533 ⋊ C2 |
| Sylow | C53 ⋊ #3131 |
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^52,h^b=h^52,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27279400, #27279416, #27279418, … |
| maximal normal subgroup of | #27279400, #27279416, #27279418, … |
| maximal quotient of | #27384284, #27386705, #27387728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14835);