Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C22⋊C9)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C22⋊C9)⋊C2)⋊C27 |
| unambiguous semidirect product | ((C22⋊C9)⋊C27)⋊C2 |
| derived | C22⋊C9 ⋊ C2×C27 |
89 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^5,2^2|b^3=c,c^3=d,e^3=f,e^a=e^2f^2,f^a=f^2,g^a=gh,e^b=ef,g^e=h,h^e=gh171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 830);