Finite Group DatabasebetaFinite Group Databasebeta| order | 4122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D229⋊C3) |
| unambiguous semidirect product | (C229⋊C3)⋊D3 |
| unambiguous semidirect product | D687⋊C3 |
| Fitting, socle, derived | C3×C229 ⋊ C2×C3 |
| Hall | C3×C229⋊C3 ⋊ C2 |
| Sylow | C229 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C229 | C2×C3 |
| LCS | G ▷ C3×C229 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 232 |
| transitive degree | μt(G) = 687 |
Polycyclic presentation:
2,3^2,229|c^a=c^2,d^a=d^228,d^b=d^134123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4122, 9);