Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D157⋊#108 |
| Sylow | C157 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^129,g^c=g^156,g^e=g^156652 conjugacy classes — view the full character table.
| maximal subgroup of | #34115195, #34115198, #34115200, … |
| maximal normal subgroup of | #34115195, #34115198, #34115200, … |
| maximal quotient of | D157⋊#334, D157⋊#335, #34115683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1562);