Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3339 |
366 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=eg,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,d^b=de,f^c=fg,h^c=h^521075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27540952, #27540954, #27541004, … |
| maximal normal subgroup of | #27540952, #27540954, #27541004, … |
| maximal quotient of | #27400345, #27401742, #27401758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16913);