Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #354 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^166,c^b=cf,d^b=def,d^c=df1175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322289, #36322290, #36322295, … |
| maximal normal subgroup of | #36322289, #36322290, #36322295, … |
| maximal quotient of | #36322072, #36322082, #36322138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 344);