Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3585 |
1464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^d=h^52613 conjugacy classes — view the full character table.
| maximal subgroup of | #27415379, #27415381, #27415401, … |
| maximal normal subgroup of | #27415379, #27415381, #27415401, … |
| maximal quotient of | #28247660, #28247672, #28247773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19286);