Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1542 |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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,b^2=g,c^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^52,d^b=dg,e^b=efg766 conjugacy classes — view the full character table.
| maximal subgroup of | #27275164, #27275167, #27275178, … |
| maximal normal subgroup of | #27275164, #27275167, #27275178, … |
| maximal quotient of | #27272039, #27272056, #27272385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3167);