Finite Group DatabasebetaFinite Group Databasebeta| order | 29070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | D5×C17×#4296 |
| unambiguous semidirect product | C5⋊(C2×C17×#4296) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D5×#4296 |
| commutator, hypocenter | C5×C19 | C2×C9×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C19 | C2×C9 |
| prime radical | D5×C17×C19⋊C3 | C3 |
| cosocle | C5×C19⋊C3 | C2×C3×C17 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1615 |
748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29070, 30);