Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #137×C167 ⋊ C2 |
| Sylow | C167 ⋊ #471 |
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|b^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^166,g^b=g^166,e^c=ef929 conjugacy classes — view the full character table.
| maximal subgroup of | #471×D167, C2×#24923534, #36333855, … |
| maximal normal subgroup of | #471×D167, C2×#24923534, #36333855, … |
| maximal quotient of | #36323481, #36323488, #36323511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 814);