Finite Group DatabasebetaFinite Group Databasebeta| order | 31746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | D11×C37×C13⋊C3 |
| unambiguous semidirect product | C11⋊(C2×C37×C13⋊C3) |
| unambiguous semidirect product | (C13×D11)⋊(C3×C37) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D11×C13⋊C3 |
| commutator, cosocle, hypocenter | C11×C13 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C37 | C2×C3 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5291 |
1813 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31746, 34);