Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#448 ⋊ C2 |
| Sylow | C53 ⋊ #3326 |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^52,c^b=cg,d^b=de,h^b=h^52,f^c=fg523 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3326, C2×#20286972, #28261042, … |
| maximal normal subgroup of | D53×#3326, C2×#20286972, #28261042, … |
| maximal quotient of | #27399722, #27400529, #27401334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16767);