Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#11927412 |
| Fitting, socle, derived, Hall | C5×C31×C61 ⋊ C4 |
| Hall | C31×C61 ⋊ AGL(1,𝔽5) |
| Hall | C5×C61 ⋊ Dic31 |
| Hall | C5×C31 ⋊ #6923 |
| Sylow | C61 ⋊ C31⋊AGL(1,𝔽5) |
| Sylow | C31 ⋊ #11927412 |
| Sylow | C5 ⋊ C31⋊#6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C31×C61 | C4 |
| prime radical, cosocle | C31×D305 | C2 |
| LCS | G ▷ C5×C31×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9455 |
Polycyclic presentation:
2^2,5,31,61|a^2=b,c^a=c^2,d^a=d^30,e^a=e^50,c^b=c^4,e^b=e^602390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 84);