Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14517896 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting | C92 ⋊ SL(2,𝔽3) |
| derived | #10619734 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #10619734 | C3 |
| Frattini, socle | C32 | PSU(3,𝔽2)⋊C3 |
| Fitting | C92 | SL(2,𝔽3) |
| LCS | G ▷ #10619734 | |
| UCS | C1 | |
35 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3,2^3,3^4|b^2=d,c^2=d,e^3=gh,f^3=g^2h,b^a=bc,c^a=b,e^a=ef^2g,f^a=fgh,g^a=h,h^a=g^2h^2,c^b=cd,e^b=fg^2,f^b=e^2g^2,g^b=h,h^b=g^2,e^c=ef^2h,f^c=e^2f^2gh,g^c=gh,h^c=gh^2,e^d=e^2g^2h^2,f^d=f^2gh^2,g^d=g^2,h^d=h^213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2290);