Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #2943 |
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^52,e^b=eg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27299379, #27299381, #27300738, … |
| maximal normal subgroup of | #27299379, #27299381, #27300738, … |
| maximal quotient of | #27353499, #27353667, #27353870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13311);