Finite Group DatabasebetaFinite Group Databasebeta| order | 34780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#10625194 |
| Fitting, socle, derived, Hall | C5×C37×C47 ⋊ C4 |
| Hall | C37×C47 ⋊ Dic5 |
| Hall | C5×C47 ⋊ #3866 |
| Hall | C5×C37 ⋊ Dic47 |
| Sylow | C47 ⋊ #10625194 |
| Sylow | C37 ⋊ Dic235 |
| Sylow | C5 ⋊ C47⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C37×C47 | C4 |
| prime radical, cosocle | C5×C47×D37 | 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^4,d^a=d^31,e^a=e^46,d^b=d^362353 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34780, 23);