Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C127 ⋊ #361 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^126,c^b=cef,d^b=df,e^b=ef898 conjugacy classes — view the full character table.
| maximal subgroup of | #361×D127, C2×#22549689, #30640476, … |
| maximal normal subgroup of | #361×D127, C2×#22549689, #30640476, … |
| maximal quotient of | #30636697, #30636745, #30636776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 362);