Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1365 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^52,c^b=cf,d^b=def,f^b=fg,h^b=h^52757 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1365, C2×#20272774, #27295376, … |
| maximal normal subgroup of | D53×#1365, C2×#20272774, #27295376, … |
| maximal quotient of | #27270884, #27271279, #27271753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2569);