Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#451 ⋊ C2 |
| Sylow | C53 ⋊ #3108 |
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,f^c=fg,h^d=h^52532 conjugacy classes — view the full character table.
| maximal subgroup of | #27356428, #27356430, #27356448, … |
| maximal normal subgroup of | #27356428, #27356430, #27356448, … |
| maximal quotient of | #27384106, #27387050, #27387090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14591);