Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×SD16×D127 |
| Fitting | C2×SD16×C127 ⋊ C2 |
| Sylow | C127 ⋊ C22×SD16 |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
910 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD16×D127, #440×D127, #30647584, … |
| maximal normal subgroup of | C4×SD16×D127, #440×D127, #30647584, … |
| maximal quotient of | C2×#102×D127, C2×#103×D127, C2×#106×D127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1320);