Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊((C22⋊C9)⋊C2))) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C36 |
| unambiguous semidirect product | C3⋊(C3⋊(C3⋊((C22⋊C9)⋊C2))) |
| derived | C33×C22⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C22⋊C9 | C2 |
| Frattini | C3 | C3⋊(C3⋊(C3⋊S4)) |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ C33×C22⋊C9 | |
| UCS | C1 | |
2220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
Polycyclic presentation:
2,3^5,2^2|b^3=f,b^a=b^2f^2,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2,g^a=gh,g^b=h,h^b=gh165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3624);