Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #475 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^126,e^c=ef1279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637916, #30637919, #30637930, … |
| maximal normal subgroup of | #30637916, #30637919, #30637930, … |
| maximal quotient of | #30638735, #30638998, #30639308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 834);