Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1947 |
256 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 129 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=f,b^2=f,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,d^b=dg,h^b=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278253, #27278254, #27278267, … |
| maximal normal subgroup of | #27278253, #27278254, #27278267, … |
| maximal quotient of | #27282670, #27282687, #27282724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5269);