Finite Group DatabasebetaFinite Group Databasebeta| order | 19431 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C17×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C32×C17 |
| Hall | C17×C127 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3×C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6477 |
2295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19431, 5);