Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92302⋊C4 |
| unambiguous semidirect product | (#4181⋊C4)⋊C3 |
| derived | C32⋊C9 ⋊ C2×C3×C4 |
| Sylow | #6891 ⋊ C2×C4 |
326 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,f^3=h,f^a=f^2h^2,g^a=g^2,h^a=h^2,e^b=e^2,g^b=g^2,f^c=fh^2,f^e=fg78 conjugacy classes — view the full character table.
| maximal subgroup of | #72229228, C4×(((C3⋊D3)⋊C9)⋊C2)⋊C3, #72247464, … |
| maximal normal subgroup of | C4×(((C3⋊D3)⋊C9)⋊C2)⋊C3, #72259310 |
| maximal quotient of | #72247464 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1201);