Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2209 |
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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=g,b^2=d,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^c=ef,f^c=fg,h^c=h^52601 conjugacy classes — view the full character table.
| maximal subgroup of | #27297548, #27297549, #27297555, … |
| maximal normal subgroup of | #27297548, #27297549, #27297555, … |
| maximal quotient of | #27298240, #27298276, #27298395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6557);