Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C127 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,b^2=f,c^2=ef,d^2=f,b^a=bd,d^a=df,d^b=df,g^c=g^126910 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q16×D127, C2×#22549968, #30647498, … |
| maximal normal subgroup of | C4×Q16×D127, C2×#22549968, #30647498, … |
| maximal quotient of | #30637534, #30637577, #30637583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 641);