Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×SD32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2187 |
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^c=h^52601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2187, C2×#20276642, #27537866, … |
| maximal normal subgroup of | D53×#2187, C2×#20276642, #27537866, … |
| maximal quotient of | #27296204, #27296548, #27297308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6437);