Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1320 |
128 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,d^b=de,d^c=dg754 conjugacy classes — view the full character table.
| maximal subgroup of | #27271442, #27271443, #27271444, … |
| maximal normal subgroup of | #27271442, #27271443, #27271444, … |
| maximal quotient of | #27270711, #27270713, #27270723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2446);