Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊#92172 |
| Fitting | C4×C32⋊C27 ⋊ C2 |
| Sylow | C32⋊C27 ⋊ D4 |
202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,e^3=g,g^3=h,b^a=bd,e^a=e^2g^2h^2,f^a=f^2,g^a=g^2h^2,h^a=h^2,e^c=ef207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 335);