Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C167 ⋊ Q64 |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^166932 conjugacy classes — view the full character table.
| maximal subgroup of | Q64×D167, C2×#24923109, #36326445, … |
| maximal normal subgroup of | Q64×D167, C2×#24923109, #36326445, … |
| maximal quotient of | #36322318, #36322319, #36322337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 389);