Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2117 |
220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 89 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,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299165, #27299167, #27299218, … |
| maximal normal subgroup of | #27299165, #27299167, #27299218, … |
| maximal quotient of | #27293163, #27293168, #27293235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6137);