Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#468 ⋊ C2 |
| Sylow | C53 ⋊ #3254 |
386 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^d=h^52442 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3254, C2×#20286097, #28256984, … |
| maximal normal subgroup of | D53×#3254, C2×#20286097, #28256984, … |
| maximal quotient of | #27394036, #27394043, #27394491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15892);