Finite Group DatabasebetaFinite Group Databasebeta| order | 1540 |
| isoclinism | isoclinic class of D5×D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D77 |
| unambiguous semidirect product | (C7×D5)⋊D11 |
| unambiguous semidirect product | (D5×C11)⋊D7 |
| Fitting, socle, derived, Hall | C5×C7×C11 ⋊ C22 |
| Hall | C7×C11 ⋊ C2×D5 |
| Hall | C5×C11 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D11 |
| Sylow | C11 ⋊ D5×D7 |
| Sylow | C7 ⋊ D5×D11 |
| Sylow | C5 ⋊ C2×D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C11 | C22 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C11⋊AGL(1,𝔽7), C3×D5×D77, D15×D77, … |
| maximal normal subgroup of | D5×C11⋊AGL(1,𝔽7), C3×D5×D77, D5×C11×D77, … |
| maximal quotient of | C3×D5×D77, D15×D77, D5×D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1540, 27);