Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#353 ⋊ C2 |
| Sylow | C53 ⋊ #1408 |
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=d,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^52,d^c=dfg,e^d=eg355 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1408, C2×#20272877, #27304402, … |
| maximal normal subgroup of | D53×#1408, C2×#20272877, #27304402, … |
| maximal quotient of | #27271474, #27271506, #27271598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2672);