Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C3⋊#10619754 |
| Fitting | C22×C32×C9 ⋊ D3 |
| derived | C3×(C3×A4)⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C9⋊S4) |
| commutator, cosocle, hypocenter | C3×(C3×A4)⋊C9 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C3×(C3×A4)⋊C9 | |
| UCS | C1 ◁ C3 | |
489 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^5,2^2|d^3=f,b^a=b^2,c^a=c^2,d^a=d^2f^2,f^a=f^2,g^a=gh,d^b=de,g^b=h,h^b=gh99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2507);