Finite Group DatabasebetaFinite Group Databasebeta| order | 3664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#11745021 |
| unambiguous semidirect product | (C2×#11745021)⋊C2 |
| Fitting | C22×C229 ⋊ C4 |
| Sylow | C229 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 916 |
Polycyclic presentation:
2^4,229|a^2=d,b^a=bc,e^a=e^122,e^d=e^228238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3664, 45);