Finite Group DatabasebetaFinite Group Databasebeta| order | 3420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| direct product | C19⋊C3×A5 |
| unambiguous semidirect product | C19⋊(C3×A5) |
| unambiguous semidirect product | (C19×A5)⋊C3 |
| Fitting, Sylow | C19 ⋊ C3×A5 |
| socle, derived | C19×A5 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C19×A5 | C3 |
| Fitting, cosocle | C19 | C3×A5 |
| LCS | G ▷ C19×A5 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 95 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C19⋊C3×A5, C7×C19⋊C3×A5, A5×#87704, … |
| maximal normal subgroup of | C5×C19⋊C3×A5, C7×C19⋊C3×A5, C11×C19⋊C3×A5 |
| maximal quotient of | C5×C19⋊C3×A5, C7×C19⋊C3×A5, A5×#87704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3420, 143);