Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2153 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^30,c^b=cg,h^e=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28311395, #28311397, #28311432, … |
| maximal normal subgroup of | #28311395, #28311397, #28311432, … |
| maximal quotient of | #28309826, #28309852, #28309882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20851);