Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3100 |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^52,f^c=fg766 conjugacy classes — view the full character table.
| maximal subgroup of | #27353955, #27353957, #27354024, … |
| maximal normal subgroup of | #27353955, #27353957, #27354024, … |
| maximal quotient of | #27384088, #27387016, #27387018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14508);