Finite Group DatabasebetaFinite Group Databasebeta| order | 34770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×D61⋊C3 |
| unambiguous semidirect product | (C5×D61)⋊(C3×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C3×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5795 |
1520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34770, 33);