Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1420 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,c^b=ceg,d^b=dg,e^b=ef,f^b=fg598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1420, C2×#20272908, #27304567, … |
| maximal normal subgroup of | D53×#1420, C2×#20272908, #27304567, … |
| maximal quotient of | #27271551, #27271656, #27271728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2703);