Finite Group Databasebeta

← Group #269566

Character table — Group #269566

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444442244444422444444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ5111111111111111111111111-1-111-1-1111-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111
χ7111111111111111111111111-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-11-1
χ101111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-1111-1
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-1-11
χ131111111111111111-1-1-1-1-1-111-1-11111-1-1-111111111-1-1-1-11111-1-1-1-1-11-11-1-1-1-111-11
χ141111111111111111-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-111-1-11-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111-1
χ1722222222222-2-2-22-22222-2-2-2-2002200-22200000000000000000000-200-200000000
χ1822222222222-2-2-22-22222-2-2-2-200-2-200-2-2-200000000000000000000200200000000
χ1922222222222-2-2-22-2-2-2-2-222-2-20022002-2-200000000000000000000200-200000000
χ2022222222222-2-2-22-2-2-2-2-222-2-200-2-20022200000000000000000000-200200000000
χ2122222222-2-2-2222-2222-2-222-2-22200-2-2-2000000000000000000000002-2000000000
χ2222222222-2-2-2222-2222-2-222-2-2-2-20022-200000000000000000000000-22000000000
χ2322222222-2-2-2222-22-2-222-2-2-2-2220022200000000000000000000000-2-2000000000
χ2422222222-2-2-2222-22-2-222-2-2-2-2-2-200-2-220000000000000000000000022000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22200000020022-2-2000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222000000200-2-22200000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000-20022-2-200000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222000000-200-2-222000000000000000000002-2000000
χ2922-222-2-2-22-2-2000202-22-20000002i−2i0002i−2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ3022-222-2-2-22-2-2000202-22-20000002i−2i0002i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ3122-222-2-2-22-2-2000202-22-2000000−2i2i000−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ3222-222-2-2-22-2-2000202-22-2000000−2i2i000−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ3322-222-2-2-22-2-200020-22-220000002i−2i000−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ3422-222-2-2-22-2-200020-22-220000002i−2i000−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ3522-222-2-2-22-2-200020-22-22000000−2i2i0002i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ3622-222-2-2-22-2-200020-22-22000000−2i2i0002i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-2-22-2-22222-222-2-2-20000002-20000000002-22-22i−2i2i−2i000000000000000000002i−2i00
χ382-2-22-2-22222-222-2-2-20000002-20000000002-22-2−2i2i−2i2i00000000000000000000−2i2i00
χ392-2-22-2-22222-222-2-2-20000002-2000000000-22-222i−2i2i−2i00000000000000000000−2i2i00
χ402-2-22-2-22222-222-2-2-20000002-2000000000-22-22−2i2i−2i2i000000000000000000002i−2i00
χ412-2-22-2-222-2-22-2-22220000002-20000000002-2-2200002-22-2000000000000002-20000
χ422-2-22-2-222-2-22-2-22220000002-20000000002-2-220000-22-2200000000000000-220000
χ432-2-22-2-222-2-22-2-22220000002-2000000000-222-200002-22-200000000000000-220000
χ442-2-22-2-222-2-22-2-22220000002-2000000000-222-20000-22-22000000000000002-20000
χ4544-444-4-4-4-444000-404-4-44000000000000000000000000000000000000000000000
χ4644-444-4-4-4-444000-40-444-4000000000000000000000000000000000000000000000
χ4744-4-4-44-440004-440-40000000000004i−4i00000000000000000000000000000000000
χ4844-4-4-44-440004-440-4000000000000−4i4i00000000000000000000000000000000000
χ4944-4-4-44-44000-44-404000000004-4000000000000000000000000000000000000000
χ5044-4-4-44-44000-44-40400000000-44000000000000000000000000000000000000000
χ514-444-44-4-44-44000-4000000000000000000000022−22−2222000000000000000000000000
χ524-444-44-4-44-44000-40000000000000000000000−222222−22000000000000000000000000
χ534-444-44-4-4-44-40004000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ544-444-44-4-4-44-4000400000000000000000000000000−2i22i22i2−2i200000000000000000000
χ554-44-44-4-440004-4-4040000000000000000000000000000022−2222−220000000000000000
χ564-44-44-4-440004-4-40400000000000000000000000000000−2222−22220000000000000000
χ574-44-44-4-44000-4440-40000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ584-44-44-4-44000-4440-4000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ594-4-44-4-44444-4-4-44-44000000-4400000000000000000000000000000000000000000
χ604-4-44-4-444-4-4444-44-4000000-4400000000000000000000000000000000000000000
χ614-4-4-4444-40000000000004i−4i000000000000000000000002-2-222i−2i−2i2i000000000000
χ624-4-4-4444-40000000000004i−4i00000000000000000000000-222-2−2i2i2i−2i000000000000
χ634-4-4-4444-4000000000000−4i4i000000000000000000000002-2-22−2i2i2i−2i000000000000
χ644-4-4-4444-4000000000000−4i4i00000000000000000000000-222-22i−2i−2i2i000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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