Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×C22⋊C16 ⋊ C2 |
| Sylow | C53 ⋊ #2187 |
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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,h^a=h^52,d^b=df,f^b=fg,h^b=h^521069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27296195, #27296196, #27296201, … |
| maximal normal subgroup of | #27296195, #27296196, #27296201, … |
| maximal quotient of | #27296208, #27296552, #27297312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6441);