Finite Group DatabasebetaFinite Group Databasebeta| order | 35742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D777 |
| unambiguous semidirect product | C3⋊(C23×D259) |
| unambiguous semidirect product | C7⋊(C23×D111) |
| unambiguous semidirect product | C37⋊(C23×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D777 |
| commutator, cosocle, hypocenter | C3×C7×C37 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C23×C37 | C2 |
| LCS | G ▷ C3×C7×C37 | |
| UCS | C1 ◁ C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17871 |
8970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35742, 18);