Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D157⋊M32 |
| Sylow | C157 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^129,g^c=g^156,g^d=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | #34115179, #34115182, #34115185, … |
| maximal normal subgroup of | #34115179, #34115182, #34115185, … |
| maximal quotient of | #34116337, #34116342, #34116343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1605);