Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×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^d=g^156289 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758189, D157⋊#360, #34116456, … |
| maximal normal subgroup of | C2×#23758189, D157⋊#360, #34116456, … |
| maximal quotient of | #34115094, #34115097, #34115122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1465);