Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1296 |
188 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^52,c^b=cg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1296, C2×#20272599, #27274177, … |
| maximal normal subgroup of | D53×#1296, C2×#20272599, #27274177, … |
| maximal quotient of | #27270644, #27270660, #27270661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2394);