Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #157⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #157⋊AGL(1,ℤ/9) |
| unambiguous semidirect product | (#157⋊D9)⋊C3 |
| Fitting, Sylow | C32×3−1+2 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C9×C3⋊D3 | C22×C3 |
| Frattini | C3 | C3×#157⋊D3 |
| Fitting | C32×3−1+2 | D4 |
| socle | C33 | C3×D12 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C9×C3⋊D3 ▷ C32×C9 | |
| UCS | C1 | |
250 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,g^3=h,b^a=bd,e^a=e^2,g^a=g^2h^2,h^a=h^2,e^b=f,f^b=e^2,g^c=gh^2,e^d=e^2,f^d=f^251 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3513);