Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C127 ⋊ #354 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^126,d^c=df706 conjugacy classes — view the full character table.
| maximal subgroup of | #354×D127, C2×#22549670, #30640392, … |
| maximal normal subgroup of | #354×D127, C2×#22549670, #30640392, … |
| maximal quotient of | #30636663, #30636673, #30636729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 343);