Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C2×C109) |
| Fitting, socle, Hall | C19×C109 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C2×C9×C109 |
| Hall | C109×#4296 ⋊ C2 |
| Hall | D19×C109 ⋊ C9 |
| Hall | #4296 ⋊ C2×C109 |
| Hall | D19 ⋊ C9×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C9×C109 |
| Frattini | C1 | G |
| Fitting, socle | C19×C109 | C2×C9 |
| prime radical | C109×D19⋊C3 | C3 |
| cosocle | C19⋊C3 | C2×C3×C109 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C109 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2071 |
2071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 27);