Finite Group DatabasebetaFinite Group Databasebeta| order | 19092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊#3866 |
| Fitting, socle, derived, Hall | C37×C43 ⋊ C3×C4 |
| Hall | C43⋊#3866 ⋊ C3 |
| Hall | C37×C43⋊C3 ⋊ C4 |
| Hall | C43⋊C3 ⋊ #3866 |
| Sylow | C43 ⋊ C3×#3866 |
| Sylow | C37 ⋊ (C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C43 | C3×C4 |
| prime radical | D37×C43⋊C3 | C2 |
| cosocle | C43×D37 | C2×C3 |
| LCS | G ▷ C37×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1591 |
Polycyclic presentation:
2,3,2,37,43|a^2=c,d^a=d^31,e^a=e^42,e^b=e^36,d^c=d^36179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19092, 35);