Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D157⋊#100 |
| Sylow | C157 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^129,e^b=ef,g^c=g^156,g^e=g^156412 conjugacy classes — view the full character table.
| maximal subgroup of | #34115219, #100×#10597845, #34115982, … |
| maximal normal subgroup of | #34115219, #100×#10597845, #34115982, … |
| maximal quotient of | D157⋊#323, #34115376, #34115377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1532);