Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C157 ⋊ C4 |
| Sylow | C157 ⋊ #327 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,c^2=f,b^a=bc,c^a=ce,g^a=g^129,c^b=cf,d^b=def,g^d=g^156409 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758124, D157⋊#327, #34115507, … |
| maximal normal subgroup of | C2×#23758124, D157⋊#327, #34115507, … |
| maximal quotient of | #34114952, #34114955, #34115009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1400);