Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic31⋊C5 |
| unambiguous semidirect product | Dic31⋊(C5×C31) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C4×C31) |
| derived | C31 ⋊ C4×C5×C31 |
| Hall | C31×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C31×Dic31 ⋊ C5 |
| Sylow | C312 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D31⋊C5 |
| commutator, hypocenter | C31 | C4×C5×C31 |
| Frattini | C2 | C31×D31⋊C5 |
| Fitting, socle | C2×C312 | C2×C5 |
| prime radical | C2×C31×ΓL(1,𝔽32) | C2 |
| cosocle | C2×C31 | C2×C5×C31 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C31 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 620 |
806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 18);