Finite Group Databasebeta

← Group #271024

Character table — Group #271024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444444448888888888888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ91111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-11-1
χ101111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-11
χ111111111111111111-1-1-1-11-1-1-1-111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1111-1-1-1-1-111-11
χ121111111111111111-1-1-1-11-1-1-1-111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111-1-1-111-1-11-1
χ131111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-1111-1
χ141111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-11
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ172222222222-2-222-2-22222-2-2-2-2-20000-222000000220000000000000000-200-200000000
χ182222222222-2-222-2-22222-2-2-2-2-20000-2-2-2000000-2-20000000000000000200200000000
χ192222222222-2-222-2-2-2-2-2-2-222220000-222000000-2-20000000000000000200-200000000
χ202222222222-2-222-2-2-2-2-2-2-222220000-2-2-2000000220000000000000000-200200000000
χ2122222222-2-222-2-22222-2-2-2-2-2222222-200-2-2-2-222000000000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-222-2-2-2-2-2002222-2-2000000000000000000000000000000
χ2322222222-2-222-2-222-2-222-222-2-22222-200-2-222-2-2000000000000000000000000000000
χ2422222222-2-222-2-222-2-222-222-2-2-2-2-2-2-20022-2-222000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2222-2-2000020000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2222-2-200002000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222-2-222000020000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222-2-22200002000000000000000000000000000-2202-2000000
χ29222-2-2-2-22002-2002-2002i−2i02i−2i0022-2-2000002i−2i000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ30222-2-2-2-22002-2002-2002i−2i02i−2i0022-2-2000002i−2i0000−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ31222-2-2-2-22002-2002-2002i−2i02i−2i00-2-22200000−2i2i000022−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ32222-2-2-2-22002-2002-2002i−2i02i−2i00-2-22200000−2i2i0000−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ33222-2-2-2-22002-2002-200−2i2i0−2i2i0022-2-200000−2i2i000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ34222-2-2-2-22002-2002-200−2i2i0−2i2i0022-2-200000−2i2i0000−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ35222-2-2-2-22002-2002-200−2i2i0−2i2i00-2-222000002i−2i000022−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ36222-2-2-2-22002-2002-200−2i2i0−2i2i00-2-222000002i−2i0000−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ372-2-22-22-2222-22-2-22-20000200002-22-2-2002-200000000002i−2i2i−2i00002i−2i2i−2i000000000000
χ382-2-22-22-2222-22-2-22-20000200002-22-2-2002-20000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ392-2-22-22-2222-22-2-22-2000020000-22-22-200-2200000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ402-2-22-22-2222-22-2-22-2000020000-22-22-200-220000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ412-2-22-22-22-2-2-22222-20000-200002-22-2200-220000002-22-200002-22-20000000000000000
χ422-2-22-22-22-2-2-22222-20000-200002-22-2200-22000000-22-220000-22-220000000000000000
χ432-2-22-22-22-2-2-22222-20000-20000-22-222002-20000002-22-20000-22-220000000000000000
χ442-2-22-22-22-2-2-22222-20000-20000-22-222002-2000000-22-2200002-22-20000000000000000
χ452-2-2-22-22200-2-200222-2000002-22-2-2200000002-2002−2−222−2−222−2−222−2−22000000000000
χ462-2-2-22-22200-2-200222-2000002-22-2-2200000002-200−222−2−222−2−222−2−222−2000000000000
χ472-2-2-22-22200-2-200222-2000002-2-222-20000000-22002−2−222−2−22−222−2−222−2000000000000
χ482-2-2-22-22200-2-200222-2000002-2-222-20000000-2200−222−2−222−22−2−222−2−22000000000000
χ492-2-2-22-22200-2-20022-2200000-222-2-220000000-22002−2−22−222−22−2−22−222−2000000000000
χ502-2-2-22-22200-2-20022-2200000-222-2-220000000-2200−222−22−2−22−222−22−2−22000000000000
χ512-2-2-22-22200-2-20022-2200000-22-222-200000002-2002−2−22−222−2−222−22−2−22000000000000
χ522-2-2-22-22200-2-20022-2200000-22-222-200000002-200−222−22−2−222−2−22−222−2000000000000
χ53444-4-4-4-4400-4400-44004i−4i0−4i4i000000000000000000000000000000000000000000000
χ54444-4-4-4-4400-4400-4400−4i4i04i−4i000000000000000000000000000000000000000000000
χ5544-444-4-4-44-4004-40000000000000000000000000000000000000000000000000022−2200
χ5644-444-4-4-44-4004-400000000000000000000000000000000000000000000000000−222200
χ5744-444-4-4-4-4400-4400000000000000000000000000000000000000000000000022−220000
χ5844-444-4-4-4-4400-44000000000000000000000000000000000000000000000000−22220000
χ594-444-4-44-44-400-4400000000000000004i−4i000000000000000000000000000000000000
χ604-444-4-44-44-400-440000000000000000−4i4i000000000000000000000000000000000000
χ614-444-4-44-4-44004-40000000000000000000000004i−4i0000000000000000000000000000
χ624-444-4-44-4-44004-4000000000000000000000000−4i4i0000000000000000000000000000
χ634-4-44-44-44444-4-4-4-440000-400000000400000000000000000000000000000000000000
χ644-4-44-44-44-4-44-444-440000400000000-400000000000000000000000000000000000000
χ654-4-4-44-444004400-4-44-400000-440000000000000000000000000000000000000000000
χ664-4-4-44-444004400-4-4-44000004-40000000000000000000000000000000000000000000
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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