Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#352 ⋊ C2 |
| Sylow | C53 ⋊ #2197 |
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^52,e^b=efg,d^c=df,h^c=h^52,e^d=eg358 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2197, C2×#20276706, #27538114, … |
| maximal normal subgroup of | D53×#2197, C2×#20276706, #27538114, … |
| maximal quotient of | #27296127, #27296134, #27296169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6501);