Finite Group DatabasebetaFinite Group Databasebeta| order | 34780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1739 |
| unambiguous semidirect product | C47⋊(C5×Dic37) |
| derived, Hall | C37×C47 ⋊ C4×C5 |
| Hall | C5×C37×C47 ⋊ C4 |
| Hall | C5×C47 ⋊ Dic37 |
| Hall | C5×C37 ⋊ Dic47 |
| Sylow | C47 ⋊ C5×Dic37 |
| Sylow | C37 ⋊ C5×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1739 |
| commutator, hypocenter | C37×C47 | C4×C5 |
| Frattini | C2 | C5×D1739 |
| Fitting, socle, prime radical | C2×C5×C37×C47 | C2 |
| cosocle | C2×C37×C47 | C2×C5 |
| LCS | G ▷ C37×C47 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34780 |
8710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34780, 4);