Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊Dic41 |
| Hall | C3×C41 ⋊ C22⋊C4 |
| Sylow | C41 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C22⋊Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×D41 |
| commutator | C2×C3×C41 | C2×C4 |
| Fitting, socle, cosocle | C22×C3×C41 | C22 |
| prime radical | C22×D3×C41 | C2 |
| hypocenter | C3×C41 | C22⋊C4 |
| LCS | G ▷ C2×C3×C41 ▷ C3×C41 | |
| UCS | C1 ◁ C22 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 984 |
Polycyclic presentation:
2^4,3,41|a^2=d,b^a=bc,f^a=f^40,e^b=e^2258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 27);