Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#103×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2898 |
726 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^d=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27400083, #27400092, #27400098, … |
| maximal normal subgroup of | #27400083, #27400092, #27400098, … |
| maximal quotient of | #27350476, #27350573, #27350574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13038);