Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1827 |
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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,c^2=d,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,f^b=fg,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299677, #27299679, #27299682, … |
| maximal normal subgroup of | #27299677, #27299679, #27299682, … |
| maximal quotient of | #27277536, #27277540, #27277544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4614);