Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #423 |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^a=g^129,g^c=g^156,g^e=g^156652 conjugacy classes — view the full character table.
| maximal subgroup of | #34115022, #34115028, #34115033, … |
| maximal normal subgroup of | #34115022, #34115028, #34115033, … |
| maximal quotient of | #34115691, #34115694, #34115697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1553);