Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C127 ⋊ C2 |
| Sylow | C127 ⋊ #474 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^126,e^c=ef,g^c=g^126901 conjugacy classes — view the full character table.
| maximal subgroup of | #474×D127, C2×#22550155, #30648516, … |
| maximal normal subgroup of | #474×D127, C2×#22550155, #30648516, … |
| maximal quotient of | #30638729, #30638974, #30638978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 828);