Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#4223) |
| Fitting | C3×C4×C41 ⋊ C4 |
| Hall | C3×C41 ⋊ C4⋊C4 |
| Sylow | C41 ⋊ C4⋊Dic3 |
| Sylow | C3 ⋊ C4⋊#4223 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 492 |
Polycyclic presentation:
2^4,3,41|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^32,f^c=f^40138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 117);