Finite Group DatabasebetaFinite Group Databasebeta| order | 1140 |
| isoclinism | isoclinic class of D15×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×D19 |
| unambiguous semidirect product | (C3×D19)⋊D5 |
| unambiguous semidirect product | (C5×D19)⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C19 ⋊ C22 |
| Hall | C5×C19 ⋊ C2×D3 |
| Hall | C3×C19 ⋊ C2×D5 |
| Sylow | C19 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D19 |
| Sylow | C5 ⋊ D3×D19 |
| Sylow | C3 ⋊ D5×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C19 | C22 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 285 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D45, D15×D19⋊C3, C3×D15×D19, … |
| maximal normal subgroup of | D15×D19⋊C3, C3×D15×D19, C11×D15×D19, … |
| maximal quotient of | D19×D45, C3×D15×D19, D19×C3⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1140, 26);