Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#324 ⋊ C2 |
| Sylow | C53 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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=e,c^2=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^52,h^c=h^52616 conjugacy classes — view the full character table.
| maximal subgroup of | #27293359, #27293361, #27293367, … |
| maximal normal subgroup of | #27293359, #27293361, #27293367, … |
| maximal quotient of | #27272050, #27272053, #27272123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2827);