Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #100×C127 ⋊ C2 |
| Sylow | C127 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^126,d^b=de,g^b=g^126,d^c=df706 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D127, C2×#22549664, #30640370, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D127, C2×#22549664, #30640370, … |
| maximal quotient of | #30636657, #30636679, #30636728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 337);