Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#568 ⋊ C2 |
| Sylow | C53 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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,f^2=g,b^a=be,e^a=eg,f^b=fg,h^b=h^52,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #27393251, #27393253, #27393257, … |
| maximal normal subgroup of | #27393251, #27393253, #27393257, … |
| maximal quotient of | #27349908, #27349923, #27349995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12988);