Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #66472⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #10620126⋊C3 |
| derived | C34 ⋊ C3×C8 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66472⋊C3 |
| commutator, hypocenter | C34 | C3×C8 |
| Frattini, socle | C2×C32 | C3×#157 |
| Fitting, prime radical | C2×C32⋊H(3,𝔽3) | C4 |
| cosocle | C3⋊(C3⋊(C3⋊Dic3)) | C2×C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,e^a=ef,f^a=ef^2,g^a=g^2h,h^a=gh,e^b=eh^2,f^b=fg^2,e^c=e^2,f^c=f^2,g^c=g^2,h^c=h^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1118);