Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C127 ⋊ #497 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^126,c^b=cf,g^b=g^126898 conjugacy classes — view the full character table.
| maximal subgroup of | #30636889, #30636891, #30638036, … |
| maximal normal subgroup of | #30636889, #30636891, #30638036, … |
| maximal quotient of | #30638351, #30638365, #30638378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 944);