Finite Group DatabasebetaFinite Group Databasebeta| order | 23142 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D609 |
| unambiguous semidirect product | C3⋊(C19×D203) |
| unambiguous semidirect product | C7⋊(C19×D87) |
| unambiguous semidirect product | C29⋊(C19×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D609 |
| commutator, cosocle, hypocenter | C3×C7×C29 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19×C29 | C2 |
| LCS | G ▷ C3×C7×C29 | |
| UCS | C1 ◁ C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11571 |
5814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23142, 20);