Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #341 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^129,g^e=g^156418 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758148, #34115829, #34115910, … |
| maximal normal subgroup of | C2×#23758148, #34115829, #34115910, … |
| maximal quotient of | #34114965, #34114967, #34114969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1424);