Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic845⋊C3) |
| unambiguous semidirect product | Dic2535⋊C3 |
| 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⋊(Dic169⋊C3) |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10140 |
Polycyclic presentation:
2,3^2,5,13,2,13|a^2=f,e^13=g^12,c^a=c^2,d^a=d^4,e^a=e^12g,g^a=g^12,e^b=e^9g^12,g^b=g^9894 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 60);