Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#10597845)⋊C8 |
| Fitting | C2×C8×C157 ⋊ C4 |
| Sylow | C157 ⋊ #336 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^129,g^e=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#10597845)⋊C8, #34115798, #34115801, … |
| maximal normal subgroup of | C2×(C2×#10597845)⋊C8, #34115798, #34115801, … |
| maximal quotient of | #34114958, #34114959, #34114961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1414);