Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived | C32×C9 ⋊ C2×C3×C4 |
| Sylow | C32×3−1+2 ⋊ C2×C4 |
602 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,g^3=h,g^a=g^2h^2,h^a=h^2,e^b=e^2,f^b=f^2,g^c=gh^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72229012, D3×(C3⋊AGL(1,ℤ/9))⋊C4, #72259553, … |
| maximal normal subgroup of | D3×(C3⋊AGL(1,ℤ/9))⋊C4, #72259553, #72259642 |
| maximal quotient of | #72229012 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3091);