Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1381 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^30,h^d=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28299067, #28299068, #28299069, … |
| maximal normal subgroup of | #28299067, #28299068, #28299069, … |
| maximal quotient of | #28298310, #28298369, #28298532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19570);