Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2262 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,h^a=h^52,d^b=de,e^b=ef,f^b=fg,h^b=h^521702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271975, #27271977, #27271978, … |
| maximal normal subgroup of | #27271975, #27271977, #27271978, … |
| maximal quotient of | #27304527, #27304595, C4×D1696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6819);