Finite Group DatabasebetaFinite Group Databasebeta| order | 31820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C43⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C43⋊(AGL(1,𝔽5)×C37) |
| Fitting, socle, Hall | C5×C37×C43 ⋊ C4 |
| derived, Hall | C5×C43 ⋊ C4×C37 |
| Hall | C37×C43 ⋊ AGL(1,𝔽5) |
| Hall | C5×C37 ⋊ Dic43 |
| Sylow | C43 ⋊ AGL(1,𝔽5)×C37 |
| Sylow | C5 ⋊ C37×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C43⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C43 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C43 | C4 |
| prime radical | D5×C37×C43 | C2 |
| cosocle | D5×C43 | C2×C37 |
| LCS | G ▷ C5×C43 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7955 |
3293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31820, 14);