Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #107×C167 ⋊ C2 |
| Sylow | C167 ⋊ #484 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,c^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^166,g^b=g^166,e^c=ef1181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #484×D167, C2×#24923606, #36334050, … |
| maximal normal subgroup of | #484×D167, C2×#24923606, #36334050, … |
| maximal quotient of | #36324227, #36324324, #36324444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 886);