Finite Group DatabasebetaFinite Group Databasebeta| order | 1140 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic19 |
| derived, Sylow | C19 ⋊ C3×C4×C5 |
| Hall | C3×C5×C19 ⋊ C4 |
| Hall | C5×C19 ⋊ C3×C4 |
| Hall | C3×C19 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D19 |
| commutator, hypocenter | C19 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D19 |
| Fitting, socle, prime radical | C2×C3×C5×C19 | C2 |
| cosocle | C2×C19 | C2×C3×C5 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1140 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#4294⋊C4, C5×C9×Dic19, C3×C5×(C19⋊C3)⋊C4, … |
| maximal normal subgroup of | C5×#4294⋊C4, C5×C9×Dic19, C3×C5×(C19⋊C3)⋊C4, … |
| maximal quotient of | C5×C9×Dic19, C32×C5×Dic19, C3×C5×Dic57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1140, 5);