Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#430 ⋊ C2 |
| Sylow | C53 ⋊ #2238 |
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,e^b=eg,d^c=dg,e^c=efg,f^c=fg592 conjugacy classes — view the full character table.
| maximal subgroup of | #27297415, #27297416, #27297426, … |
| maximal normal subgroup of | #27297415, #27297416, #27297426, … |
| maximal quotient of | #27300419, #27300659, #27301137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6724);