Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #428 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^129,c^b=cf,g^e=g^156412 conjugacy classes — view the full character table.
| maximal subgroup of | #34116091, #34116092, #34116095, … |
| maximal normal subgroup of | #34116091, #34116092, #34116095, … |
| maximal quotient of | #34115687, #34115688, #34115689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1560);