Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(#6881⋊C2) |
| Fitting | C4×#6881 ⋊ C2 |
| Sylow | #6881 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#6881⋊C2 |
| commutator, cosocle | C2×#733 | C22×C3 |
| Frattini | C2×C3×C9 | C2×C3×D3 |
| Fitting | C4×#6881 | C2 |
| socle | C2×C3 | C2×#4178 |
| hypercenter | C4 | #6881⋊C2 |
| hypocenter | #733 | C3×D4 |
| LCS | G ▷ C2×#733 ▷ #733 | |
| UCS | C1 ◁ C2 ◁ C4 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,c^3=gh^2,e^3=h^2,f^3=h^2,b^a=bd,e^a=e^2h,f^a=f^2g,g^a=gh,h^a=h^2,e^c=ef,f^c=fh,f^e=fg,g^e=gh65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 401);