Finite Group DatabasebetaFinite Group Databasebeta| order | 36822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D17×C19⋊C3 |
| unambiguous semidirect product | C17⋊(C2×C19×C19⋊C3) |
| unambiguous semidirect product | (C19×D17)⋊(C3×C19) |
| Fitting, socle, Hall | C17×C192 ⋊ C2×C3 |
| derived | C17×C19 ⋊ C2×C3×C19 |
| Hall | C17×C19×C19⋊C3 ⋊ C2 |
| Hall | C192×D17 ⋊ C3 |
| Sylow | C192 ⋊ C3×D17 |
| Sylow | C17 ⋊ C2×C19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D17×C19⋊C3 |
| commutator, cosocle, hypocenter | C17×C19 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C17×C192 | C2×C3 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C19 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 969 |
1710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36822, 23);