Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14517906 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6898 ⋊ C8 |
| derived | C92 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C92 | C3×C8 |
| Frattini, socle | C32 | C3×AGL(1,𝔽9) |
| Fitting | #6898 | C8 |
| prime radical | #92312 | C4 |
| cosocle | #66343 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
37 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3,2^2,3^4|a^2=c,c^2=d,e^3=g,f^3=h,e^a=e^2f^2h^2,f^a=e^2h,g^a=g^2h^2,h^a=g^2,e^b=eg^2h,f^b=fgh,e^c=e^2fh,f^c=efh^2,g^c=g^2h,h^c=gh,e^d=e^2g^2,f^d=f^2h^2,g^d=g^2,h^d=h^230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2300);