Finite Group DatabasebetaFinite Group Databasebeta| order | 20706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D357 |
| unambiguous semidirect product | C3⋊(C29×D119) |
| unambiguous semidirect product | C7⋊(C29×D51) |
| unambiguous semidirect product | C17⋊(C29×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D357 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C29 | C2 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C29 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10353 |
5220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20706, 17);