Finite Group DatabasebetaFinite Group Databasebeta| order | 36822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊(C17⋊(C19⋊D19)) |
| unambiguous semidirect product | C17⋊(C3⋊(C19⋊D19)) |
| unambiguous semidirect product | C19⋊D969 |
| Fitting, socle, derived, Hall | C3×C17×C192 ⋊ C2 |
| Hall | C17×C192 ⋊ D3 |
| Hall | C3×C192 ⋊ D17 |
| Sylow | C192 ⋊ D51 |
| Hall | C3×C17 ⋊ C19⋊D19 |
| Sylow | C17 ⋊ C3⋊(C19⋊D19) |
| Sylow | C3 ⋊ C17⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C192 | C2 |
| LCS | G ▷ C3×C17×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18411 |
Polycyclic presentation:
2,3,17,19^2|b^a=b^2,c^a=c^16,d^a=d^18,e^a=e^189207 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36822, 46);