Finite Group DatabasebetaFinite Group Databasebeta| order | 32418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #30633826⋊C2 |
| derived, Sylow | C1801 ⋊ C2×C9 |
| Hall | #30633826 ⋊ C2 |
| Hall | D1801 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D1801⋊C3 |
| commutator, hypocenter | C1801 | C2×C9 |
| Fitting, socle, cosocle | C3×C1801 | C2×C3 |
| prime radical | C3×D1801 | C3 |
| LCS | G ▷ C1801 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16209 |
Polycyclic presentation:
2,3,1801,3|b^3=d,c^a=c^1800,c^b=c^1727918 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32418, 2);