Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#346 ⋊ C2 |
| Sylow | C53 ⋊ #1330 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^52,c^b=ceg,d^b=dg,h^b=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1330, C2×#20272674, #27293809, … |
| maximal normal subgroup of | D53×#1330, C2×#20272674, #27293809, … |
| maximal quotient of | #27270754, #27270757, #27270760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2469);