Finite Group Databasebeta

← Group #271046

Character table — Group #271046

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111
χ61111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-11111-1-1
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-111
χ91111111111111111-1-1-1-1-1-11-1-111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111-1-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11-1-111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-11
χ121111111111111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111111-1-11-1
χ131111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1111-1
χ141111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-111-1-1-11
χ151111111111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1-1111-1-1-11
χ161111111111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1-11-1-1111-1
χ1722222222222-2-2-2-222222-2-2-2-2-20000-2000022-2-2000000000000000000-200002000000
χ1822222222222-2-2-2-222222-2-2-2-2-20000-20000-2-22200000000000000000020000-2000000
χ1922222222222-2-2-2-22-2-2-2-222-2220000-200002222000000000000000000-20000-2000000
χ2022222222222-2-2-2-22-2-2-2-222-2220000-20000-2-2-2-2000000000000000000200002000000
χ2122222222-2-2-22222-222-2-222-2-2-22222-2-2-2220000-2-20000000000000000000000000000
χ2222222222-2-2-22222-222-2-222-2-2-2-2-2-2-2-222-2-20000220000000000000000000000000000
χ2322222222-2-2-22222-2-2-222-2-2-2222222-222-2-20000-2-20000000000000000000000000000
χ2422222222-2-2-22222-2-2-222-2-2-222-2-2-2-2-2-2-2220000220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2222000020000000000000000000000000002-22-20000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222200002000000000000000000000000000-22-220000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2-2000020000000000000000000000000002-2-220000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-200002000000000000000000000000000-222-20000000
χ2922-22-2-22-2000-2-22202-2002-20002i2i−2i−2i0002i−2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ3022-22-2-22-2000-2-22202-2002-20002i2i−2i−2i0002i−2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-22-2-22-2000-2-22202-2002-2000−2i−2i2i2i000−2i2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ3222-22-2-22-2000-2-22202-2002-2000−2i−2i2i2i000−2i2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ3322-22-2-22-2000-2-2220-2200-220002i2i−2i−2i000−2i2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ3422-22-2-22-2000-2-2220-2200-220002i2i−2i−2i000−2i2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ3522-22-2-22-2000-2-2220-2200-22000−2i−2i2i2i0002i−2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ3622-22-2-22-2000-2-2220-2200-22000−2i−2i2i2i0002i−2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-22-22-22-20002-22-20002i−2i0002i−2i2i−2i2i−2i02-2000000002−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ382-22-22-22-20002-22-20002i−2i0002i−2i2i−2i2i−2i02-200000000−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ392-22-22-22-20002-22-20002i−2i0002i−2i−2i2i−2i2i0-22000000002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ402-22-22-22-20002-22-20002i−2i0002i−2i−2i2i−2i2i0-2200000000−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ412-22-22-22-20002-22-2000−2i2i000−2i2i2i−2i2i−2i0-22000000002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ422-22-22-22-20002-22-2000−2i2i000−2i2i2i−2i2i−2i0-2200000000−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ432-22-22-22-20002-22-2000−2i2i000−2i2i−2i2i−2i2i02-2000000002−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ442-22-22-22-20002-22-2000−2i2i000−2i2i−2i2i−2i2i02-200000000−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ452-2-2-2-222222-2-222-2-20000002002-2-22-2000000002-200002i−2i−2i2i0000−2i2i2i−2i000000000000
χ462-2-2-2-222222-2-222-2-20000002002-2-22-2000000002-20000−2i2i2i−2i00002i−2i−2i2i000000000000
χ472-2-2-2-222222-2-222-2-2000000200-222-2-200000000-2200002i−2i−2i2i00002i−2i−2i2i000000000000
χ482-2-2-2-222222-2-222-2-2000000200-222-2-200000000-220000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ492-2-2-2-2222-2-22-222-22000000-2002-2-22200000000-222-2-2200002-2-220000000000000000
χ502-2-2-2-2222-2-22-222-22000000-2002-2-22200000000-22-222-20000-222-20000000000000000
χ512-2-2-2-2222-2-22-222-22000000-200-222-22000000002-22-2-220000-222-20000000000000000
χ522-2-2-2-2222-2-22-222-22000000-200-222-22000000002-2-222-200002-2-220000000000000000
χ5344-44-4-44-400044-4-404-400-440000000000000000000000000000000000000000000000
χ5444-44-4-44-400044-4-40-44004-40000000000000000000000000000000000000000000000
χ5544-4-444-4-44-440000-400000000000000000000000000000000000000000000000022−2200
χ5644-4-444-4-44-440000-4000000000000000000000000000000000000000000000000−222200
χ5744-4-444-4-4-44-40000400000000000000000000000000000000000000000000002i2−2i20000
χ5844-4-444-4-4-44-4000040000000000000000000000000000000000000000000000−2i22i20000
χ594-444-44-4-44-4-4000040000000000000000004i−4i00000000000000000000000000000000
χ604-444-44-4-44-4-400004000000000000000000−4i4i00000000000000000000000000000000
χ614-444-44-4-4-4440000-4000000000000000000004-4000000000000000000000000000000
χ624-444-44-4-4-4440000-400000000000000000000-44000000000000000000000000000000
χ634-44-44-44-4000-44-440004i−4i000−4i4i0000000000000000000000000000000000000000000
χ644-44-44-44-4000-44-44000−4i4i0004i−4i0000000000000000000000000000000000000000000
χ654-4-4-4-444444-44-4-44-4000000-4000000400000000000000000000000000000000000000
χ664-4-4-4-4444-4-444-4-4440000004000000-400000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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