Finite Group DatabasebetaFinite Group Databasebeta| order | 34580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C19⋊#63122) |
| unambiguous semidirect product | C19⋊(C7⋊#63122) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C13×C19 | C4 |
| prime radical, cosocle | C7×C19×D65 | C2 |
| LCS | G ▷ C5×C7×C13×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8645 |
Polycyclic presentation:
2^2,5,7,13,19|a^2=b,c^a=c^2,d^a=d^6,e^a=e^5,f^a=f^18,c^b=c^4,e^b=e^122264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34580, 40);