Finite Group DatabasebetaFinite Group Databasebeta| order | 19220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C31 · Schur multiplier (H2) = C2 |
| direct product | C22×C31×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C22×C31)⋊(C5×C31) |
| Fitting, socle, Hall | C22×C312 ⋊ C5 |
| derived | C31 ⋊ C22×C5×C31 |
| Sylow | C312 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C31 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C22×C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C22×C312 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C31 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 620 |
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19220, 56);