Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #343 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^129,g^e=g^156412 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758152, #34115840, #100×#10597845, … |
| maximal normal subgroup of | C2×#23758152, #34115840, #100×#10597845, … |
| maximal quotient of | #34114973, #34114980, #34114982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1428);