Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | A4⋊((C3⋊D3)⋊C9) |
| Fitting | C22×C32⋊C9 ⋊ D3 |
| derived | C32×A4 ⋊ C2×C9 |
309 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 37 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:
2,3^5,2^2|b^3=c,d^a=d^2,e^a=e^2,f^a=f^2,g^a=gh,e^b=ef,g^d=h,h^d=gh93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2405);