Finite Group DatabasebetaFinite Group Databasebeta| order | 2166 |
| isoclinism | isoclinic class of C3⋊(C19⋊D19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊(C19⋊D19) |
| unambiguous semidirect product | C19⋊D57 |
| Fitting, socle, derived, Hall | C3×C192 ⋊ C2 |
| Sylow | C192 ⋊ D3 |
| Sylow | C3 ⋊ C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C192 | C2 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1083 |
Polycyclic presentation:
2,3,19^2|b^a=b^2,c^a=c^18,d^a=d^18543 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C19⋊D19, D19×D57, C2×C3⋊(C19⋊D19), … |
| maximal normal subgroup of | D3×C19⋊D19, D19×D57, C2×C3⋊(C19⋊D19), … |
| maximal quotient of | C3⋊(C19⋊Dic19), C2×C3⋊(C19⋊D19), C3⋊(C5⋊(C19⋊D19)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2166, 23);