Finite Group DatabasebetaFinite Group Databasebeta| order | 37602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #34037761⋊C2 |
| derived, Sylow | C2089 ⋊ C2×C9 |
| Hall | #34037761 ⋊ C2 |
| Hall | D2089 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D2089⋊C3 |
| commutator, hypocenter | C2089 | C2×C9 |
| Fitting, socle, cosocle | C3×C2089 | C2×C3 |
| prime radical | C3×D2089 | C3 |
| LCS | G ▷ C2089 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18801 |
Polycyclic presentation:
2,3,2089,3|b^3=d,c^a=c^2088,c^b=c^12621062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37602, 2);