Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757419⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757419⋊C2 |
| Fitting | C22×C9⋊C9 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #66358 | C2×C3 |
| Frattini | C3×C9 | C3×S4 |
| Fitting | C22×C9⋊C9 | D3 |
| socle | C22×C3 | #4178 |
| prime radical | #10619750 | C3 |
| LCS | G ▷ #66358 | |
| UCS | C1 | |
93 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^5,2^2|b^3=e^2f,d^3=f^2,c^a=c^2,d^a=d^2e,e^a=ef,f^a=f^2,g^a=gh,c^b=cd^2f,d^b=df,d^c=de,e^c=ef,g^c=h,h^c=gh53 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 824);