Finite Group DatabasebetaFinite Group Databasebeta| order | 15732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1311 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D437) |
| unambiguous semidirect product | (C2×C23)⋊(C3×D57) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1311 |
| commutator, cosocle, hypocenter | C3×C19×C23 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C19×C23 | C2 |
| LCS | G ▷ C3×C19×C23 | |
| UCS | C1 ◁ C2×C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5244 |
3942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15732, 115);