Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C127 ⋊ C2 |
| Sylow | C127 ⋊ #413 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^126,g^c=g^126715 conjugacy classes — view the full character table.
| maximal subgroup of | #30640412, #30640414, #30640420, … |
| maximal normal subgroup of | #30640412, #30640414, #30640420, … |
| maximal quotient of | #30637043, #30637047, #30637063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 532);