Finite Group DatabasebetaFinite Group Databasebeta| order | 36822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D323 |
| unambiguous semidirect product | C17⋊(D19×C19⋊C3) |
| Fitting, socle, derived, Hall | C17×C192 ⋊ C2×C3 |
| Hall | C17×C19×C19⋊C3 ⋊ C2 |
| Hall | C19×D323 ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ D17 |
| Sylow | C192 ⋊ C3×D17 |
| Sylow | C17 ⋊ D19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C192 | C2×C3 |
| LCS | G ▷ C17×C192 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1938 |
1467 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36822, 26);