Finite Group Databasebeta

← Group #266255

Character table — Group #266255

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444448888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ5111111111111111111111-1-1-1-1111-1-1-1-1111-1-11111111111-1-11-1-11-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11111
χ7111111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-11111111111-111-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111111111
χ91111111111111111-1-11-1-11111-1-1111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1111-1-111-1-111-1-1
χ101111111111111111-1-11-1-11111-1-1111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-111-1-111
χ111111111111111111-1-11-1-11111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1
χ121111111111111111-1-11-1-11111-1-1111-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-111-1-1-1-111
χ131111111111111111-1-11-1-1-1-1-1-1-1-11-1-11111-111-1-11111-1-1-1-1-1-1-1111-1-11111-1-1-1-111
χ141111111111111111-1-11-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-1-1-1111111-1111-1-1-1-1-1-11111-1-1
χ151111111111111111-1-11-1-1-1-1-1-1-1-11-1-111-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-11-1-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-1-11111-1-11-1-1-1111111-1-111-1-1
χ172222222222-2-2-222-222-2222222-2-2-2-2-22200-2-2-20000000000000000000000000000
χ182222222222-2-2-222-222-222-2-2-2-2-2-2-222-2-200-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2002220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-2-222-22222002-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2000022-2000022-200220000000000-200-2000000000000
χ2222222222-2-2222-2-2222-2-2-2000022-20000-2-2-200-2-200000000002002000000000000
χ2322222222-2-2222-2-22-2-2-2220000-2-2-2000022200-2-20000000000200-2000000000000
χ2422222222-2-2222-2-22-2-2-2220000-2-2-20000-2-2200220000000000-2002000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-20000-2-2200000020000000000000002-202-20000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-20000-2-220000002000000000000000-220-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22220000222000000-20000000000000002-20-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22220000222000000-2000000000000000-2202-20000000000
χ292222-2-2-2-222000-2-202-202-222-2-2000002-2000000022−2−222−2−2000000000000002−22−2
χ302222-2-2-2-222000-2-202-202-222-2-2000002-20000000−2−222−2−22200000000000000−22−22
χ312222-2-2-2-222000-2-202-202-2-2-22200000-22000000022−2−222−2−200000000000000−22−22
χ322222-2-2-2-222000-2-202-202-2-2-22200000-220000000−2−222−2−222000000000000002−22−2
χ332222-2-2-2-222000-2-20-220-2222-2-200000-22000000022−2−2−2−222000000000000002−2−22
χ342222-2-2-2-222000-2-20-220-2222-2-200000-220000000−2−22222−2−200000000000000−222−2
χ352222-2-2-2-222000-2-20-220-22-2-222000002-2000000022−2−2−2−22200000000000000−222−2
χ362222-2-2-2-222000-2-20-220-22-2-222000002-20000000−2−22222−2−2000000000000002−2−22
χ372-22-222-2-22-222-22-2-2002002-22-200-22-2000000000000000002-2000000002-2000000
χ382-22-222-2-22-222-22-2-2002002-22-200-22-200000000000000000-2200000000-22000000
χ392-22-222-2-22-222-22-2-200200-22-2200-2-22000000000000000002-200000000-22000000
χ402-22-222-2-22-222-22-2-200200-22-2200-2-2200000000000000000-22000000002-2000000
χ412-22-222-2-22-2-2-222-2200-2002-22-2002-2200000000000000000000000002i−2i002i−2i0000
χ422-22-222-2-22-2-2-222-2200-2002-22-2002-220000000000000000000000000−2i2i00−2i2i0000
χ432-22-222-2-22-2-2-222-2200-200-22-220022-200000000000000000000000002i−2i00−2i2i0000
χ442-22-222-2-22-2-2-222-2200-200-22-220022-20000000000000000000000000−2i2i002i−2i0000
χ454444-4-4-4-4-4-40004404-40-4400000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4000440-4404-400000000000000000000000000000000000000000000
χ4744-4-44-4-44000000000000000004i−4i0000000000002i−2i2i−2i2-22-2000000000000000000
χ4844-4-44-4-44000000000000000004i−4i000000000000−2i2i−2i2i-22-22000000000000000000
χ4944-4-44-4-4400000000000000000−4i4i0000000000002i−2i2i−2i-22-22000000000000000000
χ5044-4-44-4-4400000000000000000−4i4i000000000000−2i2i−2i2i2-22-2000000000000000000
χ5144-4-4-444-4004-4400-400000000000000000000000000022−22−2222000000000000000000
χ5244-4-4-444-4004-4400-4000000000000000000000000000−222222−22000000000000000000
χ5344-4-4-444-400-44-4004000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5444-4-4-444-400-44-400400000000000000000000000−2i22i22i2−2i20000000000000000000000
χ554-44-444-4-4-4444-4-44-400-40000000040000000000000000000000000000000000000
χ564-44-444-4-4-44-4-44-44400400000000-40000000000000000000000000000000000000
χ574-44-4-4-4444-4000-440000004-4-440000000000000000000000000000000000000000
χ584-44-4-4-4444-4000-44000000-444-40000000000000000000000000000000000000000
χ594-44-4-4-444-440004-4000000000000000000004-40000000000000000000000000000
χ604-44-4-4-444-440004-400000000000000000000-440000000000000000000000000000
χ614-4-44-44-44004-4-40040000000000000000000004-400000000000000000000000000
χ624-4-44-44-44004-4-4004000000000000000000000-4400000000000000000000000000
χ634-4-44-44-4400-44400-400000000000000004i−4i0000000000000000000000000000000
χ644-4-44-44-4400-44400-40000000000000000−4i4i0000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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