Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C167⋊C8) |
| Sylow | C167 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^166,c^b=ce1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D167, C2×Q8⋊(C167⋊C8), #36322519, … |
| maximal normal subgroup of | Q8⋊C8×D167, C2×Q8⋊(C167⋊C8), #36322519, … |
| maximal quotient of | #36321961, #36321964, #36321979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 280);