Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C167 ⋊ #479 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=df,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^166,g^b=g^166,e^c=ef,g^c=g^1661181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #479×D167, C2×#24923579, #36333924, … |
| maximal normal subgroup of | #479×D167, C2×#24923579, #36333924, … |
| maximal quotient of | #36324152, #36324393, #36324403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 859);