Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C127 ⋊ #442 |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^126,d^b=df,g^c=g^126904 conjugacy classes — view the full character table.
| maximal subgroup of | #30640629, #30640631, #442×D127, … |
| maximal normal subgroup of | #30640629, #30640631, #442×D127, … |
| maximal quotient of | #30637554, #30637595, #30637644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 661);