Finite Group DatabasebetaFinite Group Databasebeta| order | 2166 |
| isoclinism | isoclinic class of (C19⋊C3)⋊D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D19 |
| Fitting, socle, derived, Sylow | C192 ⋊ C2×C3 |
| Hall | C19×C19⋊C3 ⋊ C2 |
| Hall | C19⋊D19 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192 | C2×C3 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 57 |
Polycyclic presentation:
2,3,19^2|c^a=c^18,d^a=d^18,c^b=c^790 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2166, 13);