Finite Group Databasebeta

← Group #270821

Character table — Group #270821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222222244488888888888888161616161616161616161616161616161616163232
order12222244444444424444444444488244444448888888888848
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-11-1-1111111-1-11111-1-11-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-11-1-111111111-1-1
χ7111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-11111-1-1
χ8111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-111
χ9111111111111111-1-1-111-1111111-1-1-1-111-1-111-1-1-111-1-1-1-111-11
χ10111111111111111-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-1-11111-1-11-1
χ11111111111111111-1-1-111-111-1-1-1-111-1-111-1-1-1-111111-1-111-1-11-1
χ12111111111111111-1-1-111-111-1-1-1-111-1-1-1-111-1-1111-1-111-1-111-11
χ13111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-11
χ14111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-11111-1-1-1-1111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111-1-1111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-111-1-1-11
χ172222222222-2-2-2-2-222-200-20022-2-2-2-2000000002000000000000
χ182222222222-2-2-2-2-222-200-200-2-2222200000000-2000000000000
χ192222222222-2-2-2-2-2-2-220020022-2-22200000000-2000000000000
χ202222222222-2-2-2-2-2-2-2200200-2-222-2-2000000002000000000000
χ21222222-2-2-2-222-22-2000220-2-200000000002-200000002-2000000
χ22222222-2-2-2-222-22-2000220-2-20000000000-220000000-22000000
χ23222222-2-2-2-222-22-2000-2-202200000000002-20000000-22000000
χ24222222-2-2-2-222-22-2000-2-20220000000000-2200000002-2000000
χ252222-2-22-22-222-2-222-2-22-222-20000002-20000000000000000000
χ262222-2-22-22-222-2-222-2-2-222-22000000-220000000000000000000
χ272222-2-22-22-222-2-22-2222-2-22-2000000-220000000000000000000
χ282222-2-22-22-222-2-22-222-22-2-220000002-20000000000000000000
χ292222-2-22-22-2-2-222-22-2200-2000000000000002i−2i02i−2i0000000000
χ302222-2-22-22-2-2-222-22-2200-200000000000000−2i2i0−2i2i0000000000
χ312222-2-22-22-2-2-222-2-22-2002000000000000002i−2i0−2i2i0000000000
χ322222-2-22-22-2-2-222-2-22-200200000000000000−2i2i02i−2i0000000000
χ332222-2-2-22-22222-2-20002-20-22000000002-200000002-200000000
χ342222-2-2-22-22222-2-20002-20-2200000000-220000000-2200000000
χ352222-2-2-22-22222-2-2000-2202-2000000002-20000000-2200000000
χ362222-2-2-22-22222-2-2000-2202-200000000-2200000002-200000000
χ37444444-4-4-4-4-4-44-4400000000000000000000000000000000000
χ384444-4-4-44-44-4-4-44400000000000000000000000000000000000
χ3944-4-44-44-4-4400000000000004-40000000000000000000000000
χ4044-4-44-44-4-440000000000000-440000000000000000000000000
χ4144-4-44-4-444-4000000000000000000000000000000000022−220000
χ4244-4-44-4-444-40000000000000000000000000000000000−22220000
χ4344-4-4-4444-4-4000000000000000004-4000000000000000000000
χ4444-4-4-4444-4-400000000000000000-44000000000000000000000
χ4544-4-4-44-4-4440000000000000000000000000000000000002i2−2i200
χ4644-4-4-44-4-444000000000000000000000000000000000000−2i22i200
χ478-88-80000000000000000000004-400000000000000000000000
χ488-88-8000000000000000000000-4400000000000000000000000
χ498-8-880000008-800000000000000000000000000000000000000
χ508-8-88000000-8800000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).