Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊D109 |
| Fitting, socle, derived, Hall | C19×C109 ⋊ C2×C9 |
| Hall | C109×#4296 ⋊ C2 |
| Hall | D2071 ⋊ C9 |
| Hall | #4296 ⋊ D109 |
| Sylow | C109 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ C9×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C109 | C2×C9 |
| prime radical | (C19⋊C3)⋊D109 | C3 |
| cosocle | C19⋊C3×C109 | 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,d^b=d^4,d^c=d^7613 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 44);