Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic137 |
| Sylow | C137 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #31782638, SD32×Dic137, #31782645, … |
| maximal normal subgroup of | #31782638, SD32×Dic137, #31782645, … |
| maximal quotient of | Q16×#11764040, #31779640, #31779686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 644);