Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #127×C127 ⋊ C2 |
| Sylow | C127 ⋊ #493 |
162 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|b^2=df,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^b=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #30636892, #30637783, #30637784, … |
| maximal normal subgroup of | #30636892, #30637783, #30637784, … |
| maximal quotient of | #30638320, #30638335, #30638337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 925);