Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D27⋊C3))⋊C4 |
| unambiguous semidirect product | ((C3⋊D27)⋊C4)⋊C3 |
| derived | C3×C27 ⋊ C2×C3×C4 |
| Sylow | C3×C27⋊C3 ⋊ C2×C4 |
190 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 47 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,f^3=g,g^3=h,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,e^b=e^2,f^c=fh126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1239);