Finite Group DatabasebetaFinite Group Databasebeta| order | 37602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D6267 |
| unambiguous semidirect product | C2089⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C2089 ⋊ C2 |
| Sylow | C2089 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D2089 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C2089 | C2 |
| LCS | G ▷ C32×C2089 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18801 |
Polycyclic presentation:
2,3^2,2089|b^a=b^2,c^a=c^2,d^a=d^20889402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37602, 18);