Finite Group DatabasebetaFinite Group Databasebeta| order | 22338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(#10620321⋊C2) |
| unambiguous semidirect product | #10620321⋊D17 |
| derived, Hall | C17×C73 ⋊ C2×C9 |
| Hall | C17×#10620321 ⋊ C2 |
| Hall | D1241 ⋊ C9 |
| Hall | #10620321 ⋊ D17 |
| Sylow | C73 ⋊ C9×D17 |
| Sylow | C17 ⋊ #10620321⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C17⋊(D73⋊C3) |
| commutator, hypocenter | C17×C73 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C73 | C2×C3 |
| prime radical | C3×D1241 | C3 |
| LCS | G ▷ C17×C73 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11169 |
Polycyclic presentation:
2,3,17,73,3|b^3=e,c^a=c^16,d^a=d^72,d^b=d^8702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22338, 12);