Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14578957 |
| Sylow | C157 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^129,g^d=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#14578957, #34115087, #34115088, … |
| maximal normal subgroup of | D4⋊#14578957, #34115087, #34115088, … |
| maximal quotient of | #34115158, #34115165, #34115174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1469);