Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | 2−1+4×C127 ⋊ C2 |
| Sylow | C127 ⋊ #454 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^126,d^b=df,e^b=ef,d^c=df1087 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30640746, #30640749, #30640754, … |
| maximal normal subgroup of | #30640746, #30640749, #30640754, … |
| maximal quotient of | #30637659, #30637665, #30637670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 722);