Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×Q8×C157 ⋊ C4 |
| Sylow | C157 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,g^a=g^129,c^b=cf,d^b=def,g^b=g^156,g^d=g^156409 conjugacy classes — view the full character table.
| maximal subgroup of | D157⋊#328, C2×#23758127, #34115508, … |
| maximal normal subgroup of | D157⋊#328, C2×#23758127, #34115508, … |
| maximal quotient of | #34114955, #34114956, #34115009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1403);