Finite Group DatabasebetaFinite Group Databasebeta| order | 36822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C192 · Schur multiplier (H2) = C19 |
| direct product | C192×D51 |
| unambiguous semidirect product | C3⋊(C192×D17) |
| unambiguous semidirect product | C17⋊(D3×C192) |
| Fitting, socle, Hall | C3×C17×C192 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C2×C192 |
| Hall | C17×C192 ⋊ D3 |
| Hall | C3×C192 ⋊ D17 |
| Sylow | C17 ⋊ D3×C192 |
| Sylow | C3 ⋊ C192×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C192 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C192 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C192 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C192 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18411 |
9747 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36822, 44);