Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×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^b=g^1561576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34102026, #34102029, #34102088, … |
| maximal normal subgroup of | #34102026, #34102029, #34102088, … |
| maximal quotient of | #34101849, #34101857, #34101924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 992);