Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C127 ⋊ C2 |
| Sylow | C127 ⋊ #472 |
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,127|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^126,e^c=ef709 conjugacy classes — view the full character table.
| maximal subgroup of | #472×D127, C2×#22550144, #30648445, … |
| maximal normal subgroup of | #472×D127, C2×#22550144, #30648445, … |
| maximal quotient of | #30638083, #30638088, #30638127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 817);