Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #466 |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^c=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #30640640, #30640645, #30640650, … |
| maximal normal subgroup of | #30640640, #30640645, #30640650, … |
| maximal quotient of | #30638082, #30638087, #30638116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 782);