Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #360 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^129,c^b=cef,d^b=df,e^b=ef,g^b=g^156,g^d=g^156289 conjugacy classes — view the full character table.
| maximal subgroup of | D157⋊#360, C2×#23758190, #34116456, … |
| maximal normal subgroup of | D157⋊#360, C2×#23758190, #34116456, … |
| maximal quotient of | #34115095, #34115096, #34115123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1466);