Finite Group DatabasebetaFinite Group Databasebeta| order | 2166 |
| isoclinism | isoclinic class of D361 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D361 |
| Fitting, Hall | C3×C361 ⋊ C2 |
| derived, Sylow | C361 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D361 |
| commutator, cosocle, hypocenter | C361 | C2×C3 |
| Frattini | C19 | C3×D19 |
| Fitting | C3×C361 | C2 |
| socle | C3×C19 | D19 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 364 |
| transitive degree | μt(G) = 1083 |
546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D361, C2×C3×D361, C3×C5×D361, … |
| maximal normal subgroup of | D3×D361, C2×C3×D361, C3×C5×D361, … |
| maximal quotient of | C3×Dic361, C2×C3×D361, C3×C5×D361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2166, 5);