Finite Group DatabasebetaFinite Group Databasebeta| order | 19719 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C313 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×C313 |
| unambiguous semidirect product | C7⋊(C32×C313) |
| unambiguous semidirect product | (C3×C7)⋊(C3×C313) |
| Fitting, socle | C3×C7×C313 ⋊ C3 |
| derived, Sylow | C7 ⋊ C32×C313 |
| Hall | C7×C313 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C313 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C32×C313 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C313 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C313 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6573 |
4695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19719, 10);