Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11758281⋊D19 |
| Fitting, socle, derived, Hall | C19×C109 ⋊ C2×C9 |
| Hall | C19×#11758281 ⋊ C2 |
| Hall | D2071 ⋊ C9 |
| Hall | #11758281 ⋊ D19 |
| Sylow | C109 ⋊ C9×D19 |
| Sylow | C19 ⋊ #11758281⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C109 | C2×C9 |
| prime radical | (C109⋊C3)⋊D19 | C3 |
| cosocle | C19×C109⋊C3 | C2×C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2071 |
Polycyclic presentation:
2,3^2,19,109|b^3=c,d^a=d^18,e^a=e^108,e^b=e^16,e^c=e^63213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 63);