Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #486 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^126,g^b=g^126,g^c=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #30637819, #30637820, #30637826, … |
| maximal normal subgroup of | #30637819, #30637820, #30637826, … |
| maximal quotient of | #30638857, #30639412, #30639535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 897);