Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C127 ⋊ #365 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^126,d^b=df,g^b=g^126898 conjugacy classes — view the full character table.
| maximal subgroup of | #365×D127, C2×#22549700, #30640501, … |
| maximal normal subgroup of | #365×D127, C2×#22549700, #30640501, … |
| maximal quotient of | #30636795, #30636830, C2×#22549700 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 373);