Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #101×C167 ⋊ C2 |
| Sylow | C167 ⋊ #355 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^166,d^c=df926 conjugacy classes — view the full character table.
| maximal subgroup of | #355×D167, C2×#24923065, #36325821, … |
| maximal normal subgroup of | #355×D167, C2×#24923065, #36325821, … |
| maximal quotient of | #36322069, #36322081, #36322140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 345);