Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D157⋊(C4⋊C8) |
| Sylow | C157 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^129,g^c=g^156,g^e=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | #34114965, #34114971, #34115000, … |
| maximal normal subgroup of | #34114965, #34114971, #34115000, … |
| maximal quotient of | D157⋊#334, D157⋊#335, #34115684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1550);