Finite Group DatabasebetaFinite Group Databasebeta| order | 4044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic337⋊C3 |
| derived, Sylow | C337 ⋊ C3×C4 |
| Hall | Dic337 ⋊ C3 |
| Hall | C337⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D337⋊C3 |
| commutator, hypocenter | C337 | C3×C4 |
| Fitting, socle, cosocle | C2×C337 | C2×C3 |
| prime radical | C2×C337⋊C3 | C2 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 341 |
| transitive degree | μt(G) = 1348 |
Polycyclic presentation:
2,3,337,2|a^2=d,c^a=c^336,c^b=c^128124 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic337⋊C3, C3⋊(Dic337⋊C3), C5×Dic337⋊C3, … |
| maximal normal subgroup of | C3×Dic337⋊C3, C5×Dic337⋊C3, C7×Dic337⋊C3, … |
| maximal quotient of | Dic337⋊C9, C3×Dic337⋊C3, C3⋊(Dic337⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4044, 2);