Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#16809977⋊C3) |
| unambiguous semidirect product | (C3⋊#16809977)⋊C3 |
| Fitting, derived | C3×C5×C169 ⋊ C3×C4 |
| Hall | C3×C5×C169⋊C3 ⋊ C4 |
| Hall | C3×C169⋊C3 ⋊ Dic5 |
| Hall | C5×C169 ⋊ C3×Dic3 |
| Sylow | C169 ⋊ C3×Dic15 |
| Sylow | C5 ⋊ C3⋊(#10621721⋊C3) |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2535 |
Polycyclic presentation:
2,3,2,3,5,13^2|a^2=c,f^13=g^8,d^a=d^2,e^a=e^4,f^a=f^5g,g^a=g^5,f^b=f^3g^10,g^b=g^3,f^c=f^12g^5,g^c=g^12264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 87);