Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #2951 |
484 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 484 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,d^a=dg,e^a=eg,h^a=h^52,e^b=eg,d^c=dg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27300752, #27300756, #27300759, … |
| maximal normal subgroup of | #27300752, #27300756, #27300759, … |
| maximal quotient of | #27353574, #27353802, #27353945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13386);