Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C127 ⋊ C2 |
| Sylow | C127 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^126,d^b=de,e^b=ef,g^b=g^126,g^c=g^126715 conjugacy classes — view the full character table.
| maximal subgroup of | #30641038, #30641040, #30641044, … |
| maximal normal subgroup of | #30641038, #30641040, #30641044, … |
| maximal quotient of | #30640436, #30640511, #30640576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 982);