Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C53 ⋊ 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,h^a=h^52,d^b=dg,h^b=h^52,f^c=fg,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3120, C2×#20284935, #28252455, … |
| maximal normal subgroup of | D53×#3120, C2×#20284935, #28252455, … |
| maximal quotient of | #27384208, #27387174, #27387194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14730);