Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#485 ⋊ C2 |
| Sylow | C53 ⋊ #3093 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^52,f^c=fg,h^d=h^52526 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3093, C2×#20284647, #28251902, … |
| maximal normal subgroup of | D53×#3093, C2×#20284647, #28251902, … |
| maximal quotient of | #27383893, #27384829, #27385322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14442);