Finite Group DatabasebetaFinite Group Databasebeta| order | 19436 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#90673 |
| Fitting, socle, Hall | C43×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C4×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #90673 |
| commutator, hypocenter | C113 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C113 | C4 |
| prime radical | C43×D113 | C2 |
| cosocle | D113 | C2×C43 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C43 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4859 |
1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19436, 6);