Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | Q82×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2205 |
224 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^52,c^b=cg,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg670 conjugacy classes — view the full character table.
| maximal subgroup of | #27304859, #27304860, #27304864, … |
| maximal normal subgroup of | #27304859, #27304860, #27304864, … |
| maximal quotient of | #27296184, #27296349, #27296458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6540);