Finite Group DatabasebetaFinite Group Databasebeta| order | 2166 |
| isoclinism | isoclinic class of D361⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D361⋊C3 |
| unambiguous semidirect product | (C361⋊C3)⋊C2 |
| Fitting, derived, Sylow | C361 ⋊ C2×C3 |
| Hall | C361⋊C3 ⋊ C2 |
| Hall | D361 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C361 | C2×C3 |
| Frattini, socle | C19 | D19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 361 |
| transitive degree | μt(G) = 361 |
Polycyclic presentation:
2,3,19^2|c^19=d^18,c^a=c^18d,d^a=d^18,c^b=c^7d^4,d^b=d^766 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D361⋊C3, C5×D361⋊C3, C5⋊(D361⋊C3), … |
| maximal normal subgroup of | C2×D361⋊C3, C5×D361⋊C3, C7×D361⋊C3, … |
| maximal quotient of | (C361⋊C3)⋊C4, C2×D361⋊C3, C5×D361⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2166, 2);