Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1290 |
136 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^30,d^b=dg,h^d=h^52448 conjugacy classes — view the full character table.
| maximal subgroup of | #28298144, #28298145, #28298146, … |
| maximal normal subgroup of | #28298144, #28298145, #28298146, … |
| maximal quotient of | #28298010, #28298018, #28298059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19375);