Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^126901 conjugacy classes — view the full character table.
| maximal subgroup of | #30637906, #30637908, #30637927, … |
| maximal normal subgroup of | #30637906, #30637908, #30637927, … |
| maximal quotient of | #30638102, #30638116, #30638126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 751);