Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#541 ⋊ C2 |
| Sylow | C53 ⋊ #3120 |
372 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,f^a=fg,d^b=dg,f^c=fg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3120, C2×#20284923, #28252454, … |
| maximal normal subgroup of | D53×#3120, C2×#20284923, #28252454, … |
| maximal quotient of | #27384196, #27387162, #27387192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14718);