Finite Group DatabasebetaFinite Group Databasebeta| order | 4768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D149⋊M16 |
| Sylow | C149 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1192 |
Polycyclic presentation:
2^5,149|a^2=d,d^2=e,b^a=be,f^a=f^105,f^c=f^148,f^d=f^148316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4768, 231);