Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #101×C127 ⋊ C2 |
| Sylow | C127 ⋊ #355 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^126,d^c=df706 conjugacy classes — view the full character table.
| maximal subgroup of | #355×D127, C2×#22549672, #30640413, … |
| maximal normal subgroup of | #355×D127, C2×#22549672, #30640413, … |
| maximal quotient of | #30636661, #30636673, #30636732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 345);