Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C157 ⋊ C2 |
| Sylow | C157 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^156,d^b=de,e^b=ef,g^c=g^156874 conjugacy classes — view the full character table.
| maximal subgroup of | #510×D157, C2×#23757715, #34113269, … |
| maximal normal subgroup of | #510×D157, C2×#23757715, #34113269, … |
| maximal quotient of | #34101847, #34101854, #34101921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 991);