Finite Group DatabasebetaFinite Group Databasebeta| order | 22338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | D3×C17×C73⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C17×C73⋊C3) |
| unambiguous semidirect product | (D3×C73)⋊(C3×C17) |
| unambiguous semidirect product | (D3×C17×C73)⋊C3 |
| Fitting, socle | C3×C17×C73 ⋊ C2×C3 |
| derived | C3×C73 ⋊ C2×C3×C17 |
| Hall | C3×C17×C73⋊C3 ⋊ C2 |
| Hall | C17×C73 ⋊ C3×D3 |
| Hall | C3×C73⋊C3 ⋊ C2×C17 |
| Sylow | C73 ⋊ C3×D3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D3×C73⋊C3 |
| commutator, cosocle, hypocenter | C3×C73 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C73 | C2×C3 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 ◁ C17 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3723 |
1377 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22338, 22);