Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1298 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | #27271584, #27271585, #27271692, … |
| maximal normal subgroup of | #27271584, #27271585, #27271692, … |
| maximal quotient of | #27270645, #27270653, #27270677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2397);