Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2102 |
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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,b^2=de,c^2=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^52,f^c=fg,h^c=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | #27297469, #27297474, #27297480, … |
| maximal normal subgroup of | #27297469, #27297474, #27297480, … |
| maximal quotient of | #27289218, #27289223, #27289228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6086);