Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #6882⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6882⋊C8 |
| Sylow | #6882 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #6882⋊C2 |
| commutator, hypocenter | #733 | C3×C8 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×#6882 | C2 |
| socle | C2×C3 | #66325 |
| prime radical | C2×C32 | (C3⋊Dic3)⋊C3 |
| cosocle | C4×#733 | C2×C3 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C4 | |
61 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,b^3=gh^2,c^2=d,e^3=h^2,f^3=h^2,e^a=e^2h,f^a=f^2g,g^a=gh,h^a=h^2,e^b=ef,f^b=fh^2,f^e=fg,g^e=gh92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 49);