Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD32×D127 |
| Fitting | SD32×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×SD32 |
90 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD32×D127, #508×D127, #509×D127, … |
| maximal normal subgroup of | C2×SD32×D127, #508×D127, #509×D127, … |
| maximal quotient of | #357×D127, #358×D127, #367×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 971);