Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#367 ⋊ C2 |
| Sylow | C53 ⋊ #1418 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1418, C2×#20272901, #27304553, … |
| maximal normal subgroup of | D53×#1418, C2×#20272901, #27304553, … |
| maximal quotient of | #27271547, #27271550, #27271646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2696);