Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#557 ⋊ C2 |
| Sylow | C53 ⋊ #3371 |
344 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=e,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,c^b=cg,d^b=de,f^c=fg679 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3371, C2×#20287483, #28263908, … |
| maximal normal subgroup of | D53×#3371, C2×#20287483, #28263908, … |
| maximal quotient of | #27400778, #27400972, #27403085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17278);