Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #101×C157 ⋊ C2 |
| Sylow | C157 ⋊ #355 |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,c^2=f,d^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^156,d^c=df871 conjugacy classes — view the full character table.
| maximal subgroup of | #355×D157, C2×#23757069, #34101819, … |
| maximal normal subgroup of | #355×D157, C2×#23757069, #34101819, … |
| maximal quotient of | #34098067, #34098079, #34098138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 345);