Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #2247 |
176 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^521702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271727, #27271729, #27271739, … |
| maximal normal subgroup of | #27271727, #27271729, #27271739, … |
| maximal quotient of | #27298750, #27298782, #27298807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6763);