Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C22⋊C81)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C22⋊C81)⋊C2)⋊C3 |
| unambiguous semidirect product | #11757422⋊C2 |
| derived | C22⋊C81 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊C81 | C2×C3 |
| Frattini | C27 | C3×S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C3 | C3×D27 |
| LCS | G ▷ C22⋊C81 | |
| UCS | C1 | |
73 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^5,2^2|c^3=d,d^3=e,e^3=f,c^a=c^2d^2e^2f^2,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=gh,c^b=cf,g^c=h,h^c=gh99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 828);