Finite Group Databasebeta

← Group #290671

Character table — Group #290671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111-111-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-11-1-11111-1-1-1-1
χ91111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1111-1-111-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11-1-1-11111-1-111
χ121111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1111-1-1-1-111-1-1
χ131111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ161111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-22-222-2-200002-200000000000000000000002000-202-200000000
χ2222222222-2-22222-2-2-2-22-222-2-200002-20000000000000000000000-200020-2200000000
χ2322222222-2-22222-2-2-2-2-22-2-2220000-22000000000000000000000002000-2002-2000000
χ2422222222-2-22222-2-2-2-2-22-2-2220000-2200000000000000000000000-2000200-22000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-22200002-200000000000000000000002000-20-2200000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-22200002-20000000000000000000000-2000202-200000000
χ2722222222-2-2-2-2-2-2-2-222-2222-2-20000-22000000000000000000000002000-200-22000000
χ2822222222-2-2-2-2-2-2-2-222-2222-2-20000-2200000000000000000000000-20002002-2000000
χ2922-222-2-2-22-200002-200002i−2i2i−2i2i2i−2i−2i00002-20022−2−2i2i2−i2−i2i2i2−i2−i222−2−20000000000000000
χ3022-222-2-2-22-200002-200002i−2i2i−2i2i2i−2i−2i00002-200−2−222−i2−i2i2i2−i2−i2i2i2−2−2220000000000000000
χ3122-222-2-2-22-200002-200002i−2i2i−2i−2i−2i2i2i0000-220022−2−2i2i2−i2−i2−i2−i2i2i2−2−2220000000000000000
χ3222-222-2-2-22-200002-200002i−2i2i−2i−2i−2i2i2i0000-2200−2−222−i2−i2i2i2i2i2−i2−i222−2−20000000000000000
χ3322-222-2-2-22-200002-20000−2i2i−2i2i2i2i−2i−2i0000-220022−2−2−i2−i2i2i2i2i2−i2−i2−2−2220000000000000000
χ3422-222-2-2-22-200002-20000−2i2i−2i2i2i2i−2i−2i0000-2200−2−222i2i2−i2−i2−i2−i2i2i222−2−20000000000000000
χ3522-222-2-2-22-200002-20000−2i2i−2i2i−2i−2i2i2i00002-20022−2−2−i2−i2i2i2−i2−i2i2i222−2−20000000000000000
χ3622-222-2-2-22-200002-20000−2i2i−2i2i−2i−2i2i2i00002-200−2−222i2i2−i2−i2i2i2−i2−i2−2−2220000000000000000
χ372-222-22-2-2-2200002-2002-200002i−2i2i−2i-222i−2i000000002i−2i2i−2i00002-22-20000000000000000
χ382-222-22-2-2-2200002-2002-200002i−2i2i−2i-222i−2i00000000−2i2i−2i2i0000-22-220000000000000000
χ392-222-22-2-2-2200002-2002-20000−2i2i−2i2i-22−2i2i000000002i−2i2i−2i0000-22-220000000000000000
χ402-222-22-2-2-2200002-2002-20000−2i2i−2i2i-22−2i2i00000000−2i2i−2i2i00002-22-20000000000000000
χ412-222-22-2-2-2200002-200-2200002i−2i2i−2i2-2−2i2i00002-22-200002i−2i2i−2i00000000000000000000
χ422-222-22-2-2-2200002-200-2200002i−2i2i−2i2-2−2i2i0000-22-220000−2i2i−2i2i00000000000000000000
χ432-222-22-2-2-2200002-200-220000−2i2i−2i2i2-22i−2i00002-22-20000−2i2i−2i2i00000000000000000000
χ442-222-22-2-2-2200002-200-220000−2i2i−2i2i2-22i−2i0000-22-2200002i−2i2i−2i00000000000000000000
χ452-2-22-2-222-2-222-2-2222-20000002-2-220000002-22−2−222−2−222−2−222−2−220000000000000000
χ462-2-22-2-222-2-222-2-2222-20000002-2-220000002-2−222−2−222−2−222−2−222−20000000000000000
χ472-2-22-2-222-2-222-2-2222-2000000-222-2000000-222−2−222−2−22−222−2−222−20000000000000000
χ482-2-22-2-222-2-222-2-2222-2000000-222-2000000-22−222−2−222−22−2−222−2−220000000000000000
χ492-2-22-2-222-2-2-2-22222-220000002-2-22000000-222−2−22−222−22−2−22−222−20000000000000000
χ502-2-22-2-222-2-2-2-22222-220000002-2-22000000-22−222−22−2−22−222−22−2−220000000000000000
χ512-2-22-2-222-2-2-2-22222-22000000-222-20000002-22−2−22−222−2−222−22−2−220000000000000000
χ522-2-22-2-222-2-2-2-22222-22000000-222-20000002-2−222−22−2−222−2−22−222−20000000000000000
χ53444-4-4-44-4004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i
χ54444-4-4-44-4004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i
χ55444-4-4-44-400-44-44000000000000000000000000000000000000000000000000002i−2i−2i2i
χ56444-4-4-44-400-44-4400000000000000000000000000000000000000000000000000−2i2i2i−2i
χ5744-444-4-4-4-440000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5844-444-4-4-4-440000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ594-444-44-4-44-40000-44004400000000-4-400000000000000000000000000000000000000
χ604-444-44-4-44-40000-4400-4-4000000004400000000000000000000000000000000000000
χ614-4-44-4-4444444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ624-4-44-4-44444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ634-4-4-4444-4004-4-4400000000000000000000000000000000000000002-20000002-20000
χ644-4-4-4444-4004-4-440000000000000000000000000000000000000000-22000000-220000
χ654-4-4-4444-400-444-400000000000000000000000000000000000000002-2000000-220000
χ664-4-4-4444-400-444-40000000000000000000000000000000000000000-220000002-20000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-88-8-88000000000000000000000000000000000000000000000000000000000000

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