Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C9⋊#66775) |
| unambiguous semidirect product | C9⋊(C7⋊#66775) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C7×C9×C17 | C4 |
| Frattini | C3 | C3⋊(C7⋊#66775) |
| socle | C3×C5×C7×C17 | Dic3 |
| prime radical | C3×C7×D85 | D3 |
| cosocle | C7×C9×D85 | C2 |
| LCS | G ▷ C5×C7×C9×C17 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5355 |
Polycyclic presentation:
2^2,3,5,7,17,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^6,f^a=f^13,g^a=g^2,d^b=d^4,f^b=f^161389 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 84);