Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D81 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C81⋊C8) |
| unambiguous semidirect product | C81⋊(C3⋊C8) |
| derived, Sylow | C3×C81 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊D81 |
| commutator, hypocenter | C3×C81 | C8 |
| Frattini | C4×C27 | C3⋊D3 |
| Fitting, cosocle | C3×C4×C81 | C2 |
| socle, prime radical | C2×C32 | Dic27 |
| LCS | G ▷ C3×C81 | |
| UCS | C1 ◁ C4 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1944 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,e^3=f,f^3=g,g^3=h,d^a=d^2,e^a=e^2f^2g^2h^2,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 69);