Finite Group Databasebeta

← Group #310550

Character table — Group #310550

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-111111111-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1
χ91111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1-1111111-1-111-1
χ17222222222-222-2-2-222222-2-2000022-2-200000022-2-200000000000-20000000000000
χ18222222222-222-2-2-222222-2-20000-2-2-2-2000000-2-2220000000000020000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-200002222000000-2-22200000000000-20000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-20000-2-22200000022-2-20000000000020000000000000
χ2122222222-22-2-2222-20000-2-22222000022-2-2-2-200000000-2-20000200000000000000
χ2222222222-22-2-2222-20000-2-222220000-2-2222200000000-2-20000-200000000000000
χ2322222222-22-2-2222-20000-2-2-2-2-2-2000022-2-22200000000220000-200000000000000
χ2422222222-22-2-2222-20000-2-2-2-2-2-20000-2-222-2-200000000220000200000000000000
χ252222-2-2-2-2202-2000-222-2-20022−2−22-2000000002-20022−2−22−222−2−2000000002−200000
χ262222-2-2-2-2202-2000-222-2-20022−2−2-2200000000-220022−2−22−2−2−22200000000−2200000
χ272222-2-2-2-2202-2000-222-2-200−2−2222-2000000002-200−2−222−22−2−22200000000−2200000
χ282222-2-2-2-2202-2000-222-2-200−2−222-2200000000-2200−2−222−2222−2−2000000002−200000
χ292222-2-2-2-2202-2000-2-2-2220022−2−22-200000000-2200−2−2222−2−2−222000000002−200000
χ302222-2-2-2-2202-2000-2-2-2220022−2−2-22000000002-200−2−2222−222−2−200000000−2200000
χ312222-2-2-2-2202-2000-2-2-22200−2−2222-200000000-220022−2−2−2222−2−200000000−2200000
χ322222-2-2-2-2202-2000-2-2-22200−2−222-22000000002-20022−2−2−22−2−222000000002−200000
χ3322-2-22-2-2222-2-2-22-2200002-2000000002i−2i2i−2i0000002-22-2000000002i−2i00000000000
χ3422-2-22-2-2222-2-2-22-2200002-2000000002i−2i2i−2i000000-22-2200000000−2i2i00000000000
χ3522-2-22-2-2222-2-2-22-2200002-200000000−2i2i−2i2i0000002-22-200000000−2i2i00000000000
χ3622-2-22-2-2222-2-2-22-2200002-200000000−2i2i−2i2i000000-22-22000000002i−2i00000000000
χ3722-2-22-2-22-2222-22-2-22i−2i2i−2i-220000002i−2i2i−2i−2i2i000000000000000000002-2000000000
χ3822-2-22-2-22-2222-22-2-22i−2i2i−2i-220000002i−2i−2i2i2i−2i00000000000000000000-22000000000
χ3922-2-22-2-22-2222-22-2-2−2i2i−2i2i-22000000−2i2i2i−2i−2i2i00000000000000000000-22000000000
χ4022-2-22-2-22-2222-22-2-2−2i2i−2i2i-22000000−2i2i−2i2i2i−2i000000000000000000002-2000000000
χ4122-2-22-2-22-2-2222-22-22i−2i2i−2i2-2000000−2i2i000000000000000000000000002-2002i−2i000
χ4222-2-22-2-22-2-2222-22-22i−2i2i−2i2-2000000−2i2i00000000000000000000000000-2200−2i2i000
χ4322-2-22-2-22-2-2222-22-2−2i2i−2i2i2-20000002i−2i000000000000000000000000002-200−2i2i000
χ4422-2-22-2-22-2-2222-22-2−2i2i−2i2i2-20000002i−2i00000000000000000000000000-22002i−2i000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ464444-4-4-4-4-40-4400040000002222−22−22000000000000000000−22220000000000000000000
χ474444-4-4-4-4-40-440004000000−22−22222200000000000000000022−220000000000000000000
χ4844-4-44-4-444-4-4-44-4440000-440000000000000000000000000000000000000000000
χ4944-4-4-444-440-44000-400000000000000000000000022−22−2222000000000000000000000
χ5044-4-4-444-440-44000-4000000000000000000000000−222222−22000000000000000000000
χ5144-4-4-444-4-404-400044i−4i−4i4i000000000000000000000000000000000000000000000
χ5244-4-4-444-4-404-40004−4i4i4i−4i000000000000000000000000000000000000000000000
χ534-44-444-4-40400-4-44000000000000000000000000000000022−2222−22000000000000000
χ544-44-444-4-40400-4-440000000000000000000000000000000−2222−2222000000000000000
χ554-44-444-4-40-40044-400000004-44-4000000000000000000000000000000000000000
χ564-44-444-4-40-40044-40000000-44-44000000000000000000000000000000000000000
χ574-44-4-4-4440000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ584-44-4-4-4440000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ594-44-4-4-44400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ604-44-4-4-44400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ614-4-444-44-404004-4-40000000000000000000000000000000000000000000000022−220
χ624-4-444-44-404004-4-400000000000000000000000000000000000000000000000−22220
χ634-4-444-44-40-400-44400000000000000000004i−4i00000000000000000000000000000
χ644-4-444-44-40-400-4440000000000000000000−4i4i00000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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