Finite Group Databasebeta

← Group #324274

Character table — Group #324274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244444444888844448888888888888888888888888824882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-111-1
χ91111111111111111-1-111-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ101111111111111111-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111
χ111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ121111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-11-11-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-11-11
χ17222222222-222-2-22-222-2-2-2-222-2-222220000-2-2-2-2000000000000220000000000000000
χ18222222222-222-2-22-222-2-2-2-222-2-2-2-2-2-200002222000000000000-2-20000000000000000
χ19222222222-222-2-22-2-2-2-2-222-2-22222220000-2-222000000000000-2-20000000000000000
χ20222222222-222-2-22-2-2-2-2-222-2-222-2-2-2-2000022-2-2000000000000220000000000000000
χ2122222222-22-2-222-2222-2-2-2-2-2-222000022-2-200000000000000000000000000-22000000
χ2222222222-22-2-222-2222-2-2-2-2-2-2220000-2-222000000000000000000000000002-2000000
χ2322222222-22-2-222-22-2-2-2-22222-2-2000022-2-2000000000000000000000000002-2000000
χ2422222222-22-2-222-22-2-2-2-22222-2-20000-2-22200000000000000000000000000-22000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000002i2i−2i−2i000000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2-2-2000000000000−2i−2i2i2i00000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-222220000000000002i2i−2i−2i00000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000−2i−2i2i2i000000000000000000002i−2i0000
χ2922-2-222-2-220-2-2002000002i−2i002i−2i22-2-20000002i−2i0000i2i2−i2−i222−2−200i2i2−i2−i222−2−200000000
χ3022-2-222-2-220-2-2002000002i−2i002i−2i22-2-20000002i−2i0000−i2−i2i2i2−2−22200−i2−i2i2i2−2−22200000000
χ3122-2-222-2-220-2-2002000002i−2i002i−2i-2-222000000−2i2i0000i2i2−i2−i222−2−200−i2−i2i2i2−2−22200000000
χ3222-2-222-2-220-2-2002000002i−2i002i−2i-2-222000000−2i2i0000−i2−i2i2i2−2−22200i2i2−i2−i222−2−200000000
χ3322-2-222-2-220-2-200200000−2i2i00−2i2i22-2-2000000−2i2i0000i2i2−i2−i2−2−22200i2i2−i2−i2−2−22200000000
χ3422-2-222-2-220-2-200200000−2i2i00−2i2i22-2-2000000−2i2i0000−i2−i2i2i222−2−200−i2−i2i2i222−2−200000000
χ3522-2-222-2-220-2-200200000−2i2i00−2i2i-2-2220000002i−2i0000i2i2−i2−i2−2−22200−i2−i2i2i222−2−200000000
χ3622-2-222-2-220-2-200200000−2i2i00−2i2i-2-2220000002i−2i0000−i2−i2i2i222−2−200i2i2−i2−i2−2−22200000000
χ372-22-22-22-2202-200-202-200002-2002i−2i2i−2i000000000000i2−i2i2−i2i2−i2i2−i22i−2i2−22−22−22−200000000
χ382-22-22-22-2202-200-202-200002-2002i−2i2i−2i000000000000−i2i2−i2i2−i2i2−i2i22i−2i−22−22−22−2200000000
χ392-22-22-22-2202-200-202-200002-200−2i2i−2i2i000000000000i2−i2i2−i2i2−i2i2−i2−2i2i−22−22−22−2200000000
χ402-22-22-22-2202-200-202-200002-200−2i2i−2i2i000000000000−i2i2−i2i2−i2i2−i2i2−2i2i2−22−22−22−200000000
χ412-22-22-22-2202-200-20-220000-22002i−2i2i−2i000000000000i2−i2i2−i2−i2i2−i2i2−2i2i2−22−2−22−2200000000
χ422-22-22-22-2202-200-20-220000-22002i−2i2i−2i000000000000−i2i2−i2i2i2−i2i2−i2−2i2i−22−222−22−200000000
χ432-22-22-22-2202-200-20-220000-2200−2i2i−2i2i000000000000i2−i2i2−i2−i2i2−i2i22i−2i−22−222−22−200000000
χ442-22-22-22-2202-200-20-220000-2200−2i2i−2i2i000000000000−i2i2−i2i2i2−i2i2−i22i−2i2−22−2−22−2200000000
χ452-2-222-2-2222-22-2-2-22002-20000002i−2i−2i2i00002i−2i00000000002i−2i−2i2i0000002-2-2200000000
χ462-2-222-2-2222-22-2-2-22002-20000002i−2i−2i2i00002i−2i0000000000−2i2i2i−2i000000-222-200000000
χ472-2-222-2-2222-22-2-2-22002-2000000−2i2i2i−2i0000−2i2i00000000002i−2i−2i2i000000-222-200000000
χ482-2-222-2-2222-22-2-2-22002-2000000−2i2i2i−2i0000−2i2i0000000000−2i2i2i−2i0000002-2-2200000000
χ492-2-222-2-222-2-2222-2-200-220000002i−2i−2i2i0000−2i2i0000002-2-22000000−2i2i2i−2i000000000000
χ502-2-222-2-222-2-2222-2-200-220000002i−2i−2i2i0000−2i2i000000-222-20000002i−2i−2i2i000000000000
χ512-2-222-2-222-2-2222-2-200-22000000−2i2i2i−2i00002i−2i0000002-2-220000002i−2i−2i2i000000000000
χ522-2-222-2-222-2-2222-2-200-22000000−2i2i2i−2i00002i−2i000000-222-2000000−2i2i2i−2i000000000000
χ5344-4-444-4-4-404400-4000004i−4i00−4i4i000000000000000000000000000000000000000000
χ5444-4-444-4-4-404400-400000−4i4i004i−4i000000000000000000000000000000000000000000
χ5544-4-4-4-44404004-40-4000000000000004i−4i000000000000000000000000000000000000
χ5644-4-4-4-44404004-40-400000000000000−4i4i000000000000000000000000000000000000
χ5744-4-4-4-4440-400-440400000000000000004-40000000000000000000000000000000000
χ5844-4-4-4-4440-400-44040000000000000000-440000000000000000000000000000000000
χ594-44-44-44-4-40-4400404-40000-4400000000000000000000000000000000000000000000
χ604-44-44-44-4-40-440040-4400004-400000000000000000000000000000000000000000000
χ614-44-4-44-440400-440-400000000000000000000002i2−2i22i2−2i200000000000000000000000000
χ624-44-4-44-440400-440-40000000000000000000000−2i22i2−2i22i200000000000000000000000000
χ634-44-4-44-440-4004-404000000000000000000000022−22−222200000000000000000000000000
χ644-44-4-44-440-4004-4040000000000000000000000−222222−2200000000000000000000000000
χ654-4-444-4-44-444-4-4-44400-44000000000000000000000000000000000000000000000000
χ664-4-444-4-44-4-44-4444-4004-4000000000000000000000000000000000000000000000000
χ678888-8-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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