Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#16809981⋊C3 |
| unambiguous semidirect product | #16809981⋊C32 |
| unambiguous semidirect product | (C3×#16809981)⋊C3 |
| Fitting | C3×C5×C169 ⋊ C3×C4 |
| derived, Hall | C5×C169 ⋊ C32×C4 |
| Hall | C3×C5×C169⋊C3 ⋊ C4 |
| Hall | #16809981 ⋊ C32 |
| Hall | C3×C169⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C169 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×#10621721⋊C3 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2535 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 75);