Finite Group DatabasebetaFinite Group Databasebeta| order | 34780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#10625193 |
| Fitting, socle, derived, Hall | C5×C37×C47 ⋊ C4 |
| Hall | C37×C47 ⋊ AGL(1,𝔽5) |
| Hall | C5×C47 ⋊ Dic37 |
| Hall | C5×C37 ⋊ Dic47 |
| Sylow | C47 ⋊ #10625193 |
| Sylow | C37 ⋊ C47⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic1739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C37×C47 | C4 |
| prime radical, cosocle | D5×C37×C47 | C2 |
| LCS | G ▷ C5×C37×C47 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8695 |
Polycyclic presentation:
2^2,5,37,47|a^2=b,c^a=c^2,d^a=d^36,e^a=e^46,c^b=c^43481 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34780, 20);