Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2216 |
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^521702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271649, #27271651, #27271655, … |
| maximal normal subgroup of | #27271649, #27271651, #27271655, … |
| maximal quotient of | #27298303, #27298354, #27298422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6601);