Finite Group DatabasebetaFinite Group Databasebeta| order | 1140 |
| isoclinism | isoclinic class of D5×C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C19⋊C3 |
| unambiguous semidirect product | (C19×Dic5)⋊C3 |
| derived, Hall | C5×C19 ⋊ C3×C4 |
| Hall | C19×Dic5 ⋊ C3 |
| Hall | C5×C19⋊C3 ⋊ C4 |
| Sylow | C19 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ C4×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×C19⋊C3 |
| commutator, hypocenter | C5×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C19 | C2×C3 |
| prime radical | C2×C5×C19⋊C3 | C2 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 380 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#4296, C3×Dic5×C19⋊C3, C19⋊C3×Dic15, … |
| maximal normal subgroup of | Dic5×#4296, C3×Dic5×C19⋊C3, C11×Dic5×C19⋊C3, … |
| maximal quotient of | Dic5×#4294, C3×Dic5×C19⋊C3, C19⋊C3×Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1140, 2);