Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C127 ⋊ #458 |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^a=bd,c^a=ce,g^a=g^126,e^b=ef,d^c=df1087 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30640718, #30640719, #30640724, … |
| maximal normal subgroup of | #30640718, #30640719, #30640724, … |
| maximal quotient of | #30637716, #30637721, #30637727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 739);