Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#427 ⋊ C2 |
| Sylow | C53 ⋊ #3349 |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^52,f^c=fg757 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3349, C2×#20287241, #28262745, … |
| maximal normal subgroup of | D53×#3349, C2×#20287241, #28262745, … |
| maximal quotient of | #27400421, #27400451, #27401781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17036);