Finite Group DatabasebetaFinite Group Databasebeta| order | 19228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic209 |
| unambiguous semidirect product | C11⋊(C23×Dic19) |
| unambiguous semidirect product | C19⋊(C23×Dic11) |
| derived, Hall | C11×C19 ⋊ C4×C23 |
| Hall | C11×C19×C23 ⋊ C4 |
| Hall | C19×C23 ⋊ Dic11 |
| Hall | C11×C23 ⋊ Dic19 |
| Sylow | C19 ⋊ C23×Dic11 |
| Sylow | C11 ⋊ C23×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D209 |
| commutator, hypocenter | C11×C19 | C4×C23 |
| Frattini | C2 | C23×D209 |
| Fitting, socle, prime radical | C2×C11×C19×C23 | C2 |
| cosocle | C2×C11×C19 | C2×C23 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19228 |
4876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19228, 8);