Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2955 |
456 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^23,e^b=eg,h^c=h^30,h^f=h^52187 conjugacy classes — view the full character table.
| maximal subgroup of | #28320990, #28320991, #28320994, … |
| maximal normal subgroup of | #28320990, #28320991, #28320994, … |
| maximal quotient of | AGL(1,ℤ/8)×#88324, #28316383, #28316385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21282);