Finite Group DatabasebetaFinite Group Databasebeta| order | 2166 |
| isoclinism | isoclinic class of C361⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C361⋊C3 |
| unambiguous semidirect product | (C2×C361)⋊C3 |
| Fitting, Hall | C2×C361 ⋊ C3 |
| derived, Sylow | C361 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C2×C3 |
| Frattini | C19 | C2×C19⋊C3 |
| Fitting | C2×C361 | C3 |
| socle | C2×C19 | C19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 363 |
| transitive degree | μt(G) = 722 |
246 conjugacy classes — view the full character table.
| maximal subgroup of | (C361⋊C3)⋊C4, C4×C361⋊C3, C2×D361⋊C3, … |
| maximal normal subgroup of | (C361⋊C3)⋊C4, C4×C361⋊C3, C2×D361⋊C3, … |
| maximal quotient of | C4×C361⋊C3, C22×C361⋊C3, D5×C361⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2166, 3);