Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1324 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,d^b=deg,d^c=dg754 conjugacy classes — view the full character table.
| maximal subgroup of | #27271470, #27271471, #27271472, … |
| maximal normal subgroup of | #27271470, #27271471, #27271472, … |
| maximal quotient of | #27270727, #27270734, #27270886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2454);