Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92182 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C3×C27 ⋊ C3×C8 |
| Sylow | #6872 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92182 |
| commutator, hypocenter | C3×C27 | C3×C8 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×#6872 | C2 |
| socle | C2×C3 | #66316 |
| prime radical | C2×H(3,𝔽3) | Dic9 |
| cosocle | C3×C4×C27 | C2×C3 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C4 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,e^3=g,g^3=h,e^a=e^2g^2h^2,f^a=f^2,g^a=g^2h^2,h^a=h^2,e^b=ef,f^b=fh^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 36);