Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11929441 |
| Sylow | C157 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^129,c^b=ce,g^d=g^156418 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11929441, D157⋊(Q8⋊C8), #34115427, … |
| maximal normal subgroup of | C2×Q8⋊#11929441, D157⋊(Q8⋊C8), #34115427, … |
| maximal quotient of | #34114954, #34114956, #34114972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1398);