Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D157⋊(C22⋊C8) |
| Sylow | C157 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,157|a^2=e,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 | #34114973, #34114978, #34114998, … |
| maximal normal subgroup of | #34114973, #34114978, #34114998, … |
| maximal quotient of | D157⋊#323, D157⋊#324, #34115368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1517);