Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#449 ⋊ C2 |
| Sylow | C53 ⋊ #3219 |
396 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^52,f^c=fg520 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3219, C2×#20285750, #28255403, … |
| maximal normal subgroup of | D53×#3219, C2×#20285750, #28255403, … |
| maximal quotient of | #27393455, #27393833, #27394667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15545);