Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #11757799⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C22×H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C3×D3×A4 |
| Fitting | C22×AΣL(1,𝔽27) | C2×C3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C22×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
204 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^2,2^2,3^3|b^3=h^2,f^a=f^2,g^a=g^2h,c^b=ch^2,d^b=de,e^b=d,f^c=fg,g^f=gh56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2543);