Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #344 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^166,d^b=df,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #344×D167, C2×#24923041, #36323939, … |
| maximal normal subgroup of | #344×D167, C2×#24923041, #36323939, … |
| maximal quotient of | #36321982, #36321984, #36321989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 321);