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 30 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 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^30,d^b=de,h^b=h^52,d^c=dg,h^d=h^52286 conjugacy classes — view the full character table.
| maximal subgroup of | #28299011, #28299012, #28299013, … |
| maximal normal subgroup of | #28299011, #28299012, #28299013, … |
| maximal quotient of | #28298093, #28298095, #28298105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19443);