Finite Group DatabasebetaFinite Group Databasebeta| order | 19803 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23×C41 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C7×C23×C41 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C23×C41 |
| Hall | C7×C41 ⋊ C3×C23 |
| Hall | C7×C23 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C41 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C23×C41 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C41 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C23×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6601 |
4715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19803, 2);