Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C3⋊((C3⋊D3)⋊(C22⋊C9)) |
| derived | C22×C33 ⋊ C2×C9 |
572 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 51 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:
2,3^2,2^2,3^3|b^3=c,f^a=f^2,g^a=g^2,h^a=h^2,d^b=de,e^b=d,g^b=gh108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2656);