Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2161 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^52,c^b=cg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299519, #27299524, #27300619, … |
| maximal normal subgroup of | #27299519, #27299524, #27300619, … |
| maximal quotient of | #27295681, #27295745, #27295773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6305);