Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C127 ⋊ #331 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,c^2=f,d^2=ef,b^a=bc,c^a=ce,g^a=g^126,c^b=cf,d^b=def901 conjugacy classes — view the full character table.
| maximal subgroup of | #30636874, #30636875, #331×D127, … |
| maximal normal subgroup of | #30636874, #30636875, #331×D127, … |
| maximal quotient of | #30636551, #30636613, #30636767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 293);