Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C3 |
| direct product | C169×C3⋊Dic15 |
| unambiguous semidirect product | C3⋊(Dic15×C169) |
| derived, Hall | C32×C5 ⋊ C4×C169 |
| Hall | C32×C5×C169 ⋊ C4 |
| Hall | C32×C169 ⋊ Dic5 |
| Hall | C5×C169 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic5×C169 |
| Sylow | C5 ⋊ C3⋊Dic3×C169 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30420 |
8112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 71);