Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1377 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^30,d^b=dg,h^d=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298191, #28298192, #28298229, … |
| maximal normal subgroup of | #28298191, #28298192, #28298229, … |
| maximal quotient of | #28298262, #28298273, #28298284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19557);