Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1333 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^30,c^b=ceg,d^b=dg,e^b=eg,h^d=h^52214 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289673, D53⋊#1333, #28308497, … |
| maximal normal subgroup of | C2×#20289673, D53⋊#1333, #28308497, … |
| maximal quotient of | #28298124, #28298132, #28298205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19468);