Finite Group DatabasebetaFinite Group Databasebeta| order | 1540 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×D7 |
| unambiguous semidirect product | (C7×D5)⋊(C2×C11) |
| unambiguous semidirect product | (C5×D7)⋊(C2×C11) |
| unambiguous semidirect product | D35⋊(C2×C11) |
| Fitting, socle, Hall | C5×C7×C11 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C22×C11 |
| Hall | C7×C11 ⋊ C2×D5 |
| Hall | C5×C11 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D5×C11 |
| Sylow | C5 ⋊ C2×C11×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C11×AGL(1,𝔽7), C3×D5×C11×D7, C11×D7×D15, … |
| maximal normal subgroup of | D5×C11×AGL(1,𝔽7), C3×D5×C11×D7, D5×D7×C121, … |
| maximal quotient of | C3×D5×C11×D7, C11×D7×D15, D5×C11×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1540, 25);