Finite Group DatabasebetaFinite Group Databasebeta| order | 37140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C619⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C619⋊AGL(1,𝔽5))⋊C3 |
| Fitting, socle, derived, Hall | C5×C619 ⋊ C3×C4 |
| Hall | C619⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×C619⋊C3 ⋊ C4 |
| Hall | C619⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C619 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ (C619⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C619 | C3×C4 |
| prime radical | D5×C619⋊C3 | C2 |
| cosocle | D5×C619 | C2×C3 |
| LCS | G ▷ C5×C619 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3095 |
Polycyclic presentation:
2,3,2,5,619|a^2=c,d^a=d^2,e^a=e^618,e^b=e^366,d^c=d^4427 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37140, 14);