Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊D27)) |
| Fitting | C32×C4×C27 ⋊ C2 |
| Sylow | C32×C27 ⋊ D4 |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 972 |
Polycyclic presentation:
2^3,3^5|b^2=c,f^3=g,g^3=h,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2489 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2127);