Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(#733⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊(#733⋊C8) |
| derived, Sylow | C3×#733 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊(#733⋊C2) |
| commutator, hypocenter | C3×#733 | C8 |
| Frattini | C32×C4 | C3⋊(C3⋊D3) |
| Fitting, cosocle | C3×C4×#733 | C2 |
| socle | C2×C32 | #1084 |
| prime radical | C2×C33 | C3⋊Dic3 |
| LCS | G ▷ C3×#733 | |
| UCS | C1 ◁ C4 | |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,e^3=h,f^3=h,d^a=d^2,e^a=e^2h^2,f^a=f^2h^2,g^a=gh^2,h^a=h^2,f^e=fg,g^f=gh120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 770);