Finite Group DatabasebetaFinite Group Databasebeta| order | 1540 |
| isoclinism | isoclinic class of D7×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×D11 |
| Fitting, socle, Hall | C5×C7×C11 ⋊ C22 |
| derived, Hall | C7×C11 ⋊ C22×C5 |
| Hall | C5×C11 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C5×D7 |
| Sylow | C7 ⋊ C2×C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×D11 |
| commutator, cosocle, hypocenter | C7×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C22 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D11×AGL(1,𝔽7), C3×C5×D7×D11, C5×D11×D21, … |
| maximal normal subgroup of | C5×D11×AGL(1,𝔽7), C3×C5×D7×D11, C5×C11×D7×D11, … |
| maximal quotient of | C3×C5×D7×D11, C5×D11×D21, C5×D7×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1540, 22);