Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1508 |
294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,c^2=g,d^2=g,b^a=bd,d^a=df,h^a=h^52,c^b=cf,d^b=dg,e^b=efg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27275694, #27275696, #27275699, … |
| maximal normal subgroup of | #27275694, #27275696, #27275699, … |
| maximal quotient of | #27272082, #27272091, #27272130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3031);