Finite Group DatabasebetaFinite Group Databasebeta| order | 34780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D185⋊D47 |
| unambiguous semidirect product | D235⋊D37 |
| unambiguous semidirect product | D1739⋊D5 |
| Fitting, socle, derived, Hall | C5×C37×C47 ⋊ C22 |
| Hall | C37×C47 ⋊ C2×D5 |
| Hall | C5×C47 ⋊ C2×D37 |
| Hall | C5×C37 ⋊ C2×D47 |
| Sylow | C47 ⋊ D5×D37 |
| Sylow | C37 ⋊ D5×D47 |
| Sylow | C5 ⋊ D37×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C37×C47 | C22 |
| LCS | G ▷ C5×C37×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8695 |
Polycyclic presentation:
2^2,5,37,47|d^a=d^36,e^a=e^46,c^b=c^4,d^b=d^362242 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34780, 28);