Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1424 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=ceg,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^b=h^52610 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1424, C2×#20272916, #27304592, … |
| maximal normal subgroup of | D53×#1424, C2×#20272916, #27304592, … |
| maximal quotient of | #27271770, #27271792, #27271997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2711);