Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32×3−1+2 ⋊ D4 |
650 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 81 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|b^2=d,g^3=h,b^a=bd,g^a=g^2h^2,h^a=h^2,e^b=e^2,f^b=f^2,g^c=gh^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #72229044, #72259522, #72259553, … |
| maximal normal subgroup of | #72259522, #72259553, D3×#6192⋊C3 |
| maximal quotient of | #72229044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3093);