Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C9×C23⋊Dic23 |
| unambiguous semidirect product | C23⋊(C9×Dic23) |
| derived, Sylow | C232 ⋊ C4×C9 |
| Hall | C9×C232 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | C23⋊D23 |
| commutator, hypocenter | C232 | C4×C9 |
| Frattini | C2×C3 | C3×C23⋊D23 |
| Fitting | C2×C9×C232 | C2 |
| socle, prime radical, cosocle | C2×C3×C232 | C2×C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C2×C9 | |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19044 |
4788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 36);