Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D81⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D81⋊A4 |
| unambiguous semidirect product | (C81⋊A4)⋊C2 |
| Fitting, derived | C22×C81 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C81 | C2×C3 |
| Frattini | C27 | D3×A4 |
| socle | C22×C3 | C3×D27 |
| LCS | G ▷ C22×C81 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3,2^2,3^4|e^3=f^2,f^3=g^2,g^3=h^2,e^a=e^2fgh,f^a=f^2gh,g^a=g^2h,h^a=h^2,c^b=d,d^b=cd,e^b=eh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 897);