Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,g^a=g^126,c^b=cf,d^b=def901 conjugacy classes — view the full character table.
| maximal subgroup of | #328×D127, C2×#22549613, #30637215, … |
| maximal normal subgroup of | #328×D127, C2×#22549613, #30637215, … |
| maximal quotient of | #30636553, #30636556, #30636608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 286);