Finite Group DatabasebetaFinite Group Databasebeta| order | 15708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | D3×C17×D77 |
| unambiguous semidirect product | (D3×C7)⋊(C17×D11) |
| unambiguous semidirect product | (D3×C11)⋊(D7×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D3×D77 |
| commutator, cosocle, hypocenter | C3×C7×C11 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C17 | C22 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C17 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3927 |
2040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15708, 79);