Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16861235 |
| Fitting | C22×D4×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×AGL(1,ℤ/8) |
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.
1282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30639103, #30639109, #30639207, … |
| maximal normal subgroup of | #30639103, #30639109, #30639207, … |
| maximal quotient of | C2×#22549881, C2×#22549875, C2×#22549916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1336);