Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×#10587739 |
| Fitting | Q16×C137 ⋊ C4 |
| Sylow | C137 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#10587739, Q32×#10587739, #31797185, … |
| maximal normal subgroup of | SD32×#10587739, Q32×#10587739, #31797185, … |
| maximal quotient of | Q16×#11764047, #31796376, #31796377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1587);