Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C127 ⋊ #487 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^c=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #487×D127, C2×#22550225, #30649050, … |
| maximal normal subgroup of | #487×D127, C2×#22550225, #30649050, … |
| maximal quotient of | #30638856, #30639403, #30639404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 898);