Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C127 ⋊ C2 |
| Sylow | C127 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^126,g^c=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #428×D127, C2×#22549917, #30647317, … |
| maximal normal subgroup of | #428×D127, C2×#22549917, #30647317, … |
| maximal quotient of | #30637481, #30637496, #30637514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 590);