Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊S4)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | (C3⋊S4)⋊C27 |
| Fitting | C22×C3×C27 ⋊ D3 |
| derived | C3×A4 ⋊ C2×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | (C3⋊S4)⋊C3 |
| commutator, hypocenter | C3×A4 | C2×C27 |
| Frattini | C3×C9 | C3×S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | D3×C9 |
| prime radical | C3×C3⋊S4 | C9 |
| cosocle | C3×C9×A4 | C2×C3 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C9 | |
107 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 107 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^5,2^2|b^3=c,c^3=d,e^a=e^2,f^a=f^2,g^a=gh,e^b=ef^2,g^e=h,h^e=gh171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 831);