Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/27) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6875⋊C8 |
| derived | C27 ⋊ C8×C9 |
| Sylow | #6875 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | AGL(1,ℤ/27) |
| commutator, hypocenter | C27 | C8×C9 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×#6875 | C2 |
| socle | C2×C3 | Dic9⋊C9 |
| prime radical | C2×C32 | 3−1+2⋊C4 |
| cosocle | C4×C27⋊C3 | C2×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3,2,3,2,3^3|a^2=c,b^3=d,c^2=e,f^3=g,g^3=h,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,f^b=fg^2h,g^b=gh^2,f^d=fh^2124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 40);