Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#11924586 |
| Sylow | C37 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4736 |
Polycyclic presentation:
2^7,37|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^31,h^d=h^36368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 19667);