Finite Group DatabasebetaFinite Group Databasebeta| order | 22338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C17⋊(D73⋊C3)) |
| unambiguous semidirect product | C17⋊(C3⋊(D73⋊C3)) |
| unambiguous semidirect product | (C73⋊C3)⋊D51 |
| unambiguous semidirect product | D3723⋊C3 |
| Fitting, socle, derived | C3×C17×C73 ⋊ C2×C3 |
| Hall | C3×C17×C73⋊C3 ⋊ C2 |
| Hall | C17×C73 ⋊ C3×D3 |
| Hall | C3×C73⋊C3 ⋊ D17 |
| Sylow | C73 ⋊ C3×D51 |
| Sylow | C17 ⋊ C3⋊(D73⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C73 | C2×C3 |
| LCS | G ▷ C3×C17×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3723 |
Polycyclic presentation:
2,3^2,17,73|c^a=c^2,d^a=d^16,e^a=e^72,e^b=e^8693 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22338, 23);