Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14516441 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C9 |
No aliases for this group.
| derived | C9×C22⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×C22⋊C9 | C2×C3 |
| Frattini | C3×C9 | C3×S4 |
| Fitting | C22×#732 | D3 |
| socle | C22×C3 | #4179 |
| LCS | G ▷ C9×C22⋊C9 | |
| UCS | C1 | |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^5,2^2|c^3=e,d^3=f,c^a=c^2e^2,d^a=d^2f^2,e^a=e^2,f^a=f^2,g^a=gh,c^b=cd^2f^2,d^b=def^2,e^b=ef^2,g^c=h,h^c=gh35 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 835);