Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C31⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C31⋊(AGL(1,𝔽5)×C31) |
| Fitting, socle, Hall | C5×C312 ⋊ C4 |
| derived | C5×C31 ⋊ C4×C31 |
| Sylow | C312 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ C31×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C31⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C31 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C312 | C4 |
| prime radical | D5×C312 | C2 |
| cosocle | D5×C31 | C2×C31 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C31 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 310 |
2015 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 64);