Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D27⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757425⋊C2 |
| derived | C22×C27 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D27⋊A4 |
| commutator, hypocenter | C22×C27 | C2×C9 |
| Frattini | C3×C9 | D3×A4 |
| Fitting, cosocle | C22×C3×C27 | C2×C3 |
| socle | C22×C32 | C3×D9 |
| prime radical | C22×C3×D27 | C3 |
| LCS | G ▷ C22×C27 | |
| UCS | C1 ◁ C3 | |
101 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^2,2^2,3^3|b^3=c,f^3=g,g^3=h,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,d^b=de,e^b=d,f^b=fh108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 913);