Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C9⋊#157) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊(C9⋊#622) |
| unambiguous semidirect product | C9⋊(C3⋊#622) |
| derived, Sylow | C33×C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C9⋊#157) |
| commutator, hypocenter | C33×C9 | C8 |
| Frattini | C2×C3 | C3⋊(C3⋊#157) |
| Fitting | C2×C33×C9 | C4 |
| socle, prime radical | C2×C34 | Dic3 |
| cosocle | C3×C9×C3⋊Dic3 | C2 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
308 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,g^3=h,d^a=de,e^a=de^2,f^a=f^2,g^a=g^2h^2,h^a=h^2,d^b=d^2,e^b=e^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2990);