Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊D27) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊(C3⋊(C27⋊C8)) |
| unambiguous semidirect product | C27⋊(C3⋊(C3⋊C8)) |
| derived, Sylow | C32×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊(C3⋊D27) |
| commutator, hypocenter | C32×C27 | C8 |
| Frattini | C4×C9 | C3⋊(C3⋊D3) |
| Fitting, cosocle | C32×C4×C27 | C2 |
| socle, prime radical | C2×C33 | Dic9 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 ◁ C4 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1944 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,f^3=g,g^3=h,d^a=d^2,e^a=e^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, 766);