Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#346 ⋊ C2 |
| Sylow | C53 ⋊ #2251 |
178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 61 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=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^52,c^b=cg1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27297588, #27297589, #27297595, … |
| maximal normal subgroup of | #27297588, #27297589, #27297595, … |
| maximal quotient of | #27298767, #27298772, #27298791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6781);