Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#390 ⋊ C2 |
| Sylow | C53 ⋊ #2054 |
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^52,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2054, C2×#20276025, #27412040, … |
| maximal normal subgroup of | D53×#2054, C2×#20276025, #27412040, … |
| maximal quotient of | #27287881, #27287883, #27287888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5820);