Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic167 |
| Sylow | C167 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36325987, SD32×Dic167, #36325994, … |
| maximal normal subgroup of | #36325987, SD32×Dic167, #36325994, … |
| maximal quotient of | Q16×C167⋊C8, #36322989, #36323035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 644);