Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1524 |
234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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=f,d^2=g,e^2=f,b^a=bd,d^a=df,h^a=h^30,d^b=dg,e^b=efg,h^b=h^52,h^c=h^52,h^e=h^52220 conjugacy classes — view the full character table.
| maximal subgroup of | #28301960, #28301968, #28301976, … |
| maximal normal subgroup of | #28301960, #28301968, #28301976, … |
| maximal quotient of | #28299413, #28299418, #28299431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19963);