Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #6878⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #6878⋊C8 |
| derived | C92 ⋊ C3×C8 |
| Sylow | #6878 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #6878⋊C2 |
| commutator, hypocenter | C92 | C3×C8 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×#6878 | C2 |
| socle | C2×C3 | #66326 |
| prime radical | C2×#732 | Dic3 |
| cosocle | C4×C92 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,e^3=g,f^3=h,e^a=e^2g^2,f^a=f^2h^2,g^a=g^2,h^a=h^2,e^b=ef,f^b=fg^2,g^b=gh88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 44);