Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2248 |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=dfg,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 | #27297532, #27297533, #27297539, … |
| maximal normal subgroup of | #27297532, #27297533, #27297539, … |
| maximal quotient of | #27298755, #27298778, #27298782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6766);