Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×(C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #6289⋊C9 |
| derived | C33 ⋊ C2×C4×C9 |
| Sylow | C3×C32⋊C9 ⋊ C2×C4 |
315 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 58 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,c^3=e,g^a=g^2,h^a=h^2,f^b=f^2,g^c=gh180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1151);