Finite Group Databasebeta

← Group #317005

Character table — Group #317005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888882222444444448888888888888888824884488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1111111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1111-1-111111111-1-1111111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-1111-1-111111111-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11
χ11111111111111-1-1-1-1111-1-111111111-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-11
χ12111111111111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111111111-1-1111-1-11
χ17222222222-2-222222-2-2-2-2-200000000222200-2-222-2-200-2000000000000000000000000
χ18222222222-2-222222-2-2-2-2-20000000022-2-20022-2-22200-2000000000000000000000000
χ19222222222-2-22-2-2-2-2-2-2-22200000000-2-22200-2-2-2-222002000000000000000000000000
χ20222222222-2-22-2-2-2-2-2-2-22200000000-2-2-2-2002222-2-2002000000000000000000000000
χ21222222-2-2-2-2-2-200002-22002i2i2i2i−2i−2i−2i−2i000022000000-2-200000000000000000002i−2i0000
χ22222222-2-2-2-2-2-200002-22002i2i2i2i−2i−2i−2i−2i0000-2-2000000220000000000000000000−2i2i0000
χ23222222-2-2-2-2-2-200002-2200−2i−2i−2i−2i2i2i2i2i000022000000-2-20000000000000000000−2i2i0000
χ24222222-2-2-2-2-2-200002-2200−2i−2i−2i−2i2i2i2i2i0000-2-20000002200000000000000000002i−2i0000
χ252222-2-22-2-22222222-2-222222-2-222-2-2-2-2000000000000-200000000000022-2-200000000
χ262222-2-22-2-22222222-2-2222-2-222-2-222-2-2000000000000-2000000000000-2-22200000000
χ272222-2-22-2-2222-2-2-2-2-2-22-2-222-2-222-2-2220000000000002000000000000-2-22200000000
χ282222-2-22-2-2222-2-2-2-2-2-22-2-2-2-222-2-22222000000000000200000000000022-2-200000000
χ292222-2-22-2-2-2-22222222-2-2-200000000-2-200000000000022i2i−2i−2i2i2i−2i−2i0000000000000000
χ302222-2-22-2-2-2-22222222-2-2-200000000-2-20000000000002−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-22-2-2-2-22-2-2-2-222-2220000000022000000000000-22i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-22-2-2-2-22-2-2-2-222-2220000000022000000000000-2−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-222-2-2-20000-222002i2i−2i−2i−2i−2i2i2i000000000000000000000002i2i−2i−2i00002-2000000
χ342222-2-2-222-2-2-20000-222002i2i−2i−2i−2i−2i2i2i00000000000000000000000−2i−2i2i2i0000-22000000
χ352222-2-2-222-2-2-20000-22200−2i−2i2i2i2i2i−2i−2i000000000000000000000002i2i−2i−2i0000-22000000
χ362222-2-2-222-2-2-20000-22200−2i−2i2i2i2i2i−2i−2i00000000000000000000000−2i−2i2i2i00002-2000000
χ372-2-222-222-200-22i2i−2i−2i00000i2−i2i2−i2i2−i2i2−i22i−2i00002i−2i002-20002−22−2i2−i2i2−i200002−22−200000000
χ382-2-222-222-200-22i2i−2i−2i00000i2−i2i2−i2i2−i2i2−i22i−2i0000−2i2i00-22000−22−22−i2i2−i2i200002−22−200000000
χ392-2-222-222-200-22i2i−2i−2i00000−i2i2−i2i2−i2i2−i2i22i−2i00002i−2i002-2000−22−22−i2i2−i2i20000−22−2200000000
χ402-2-222-222-200-22i2i−2i−2i00000−i2i2−i2i2−i2i2−i2i22i−2i0000−2i2i00-220002−22−2i2−i2i2−i20000−22−2200000000
χ412-2-222-222-200-2−2i−2i2i2i00000i2−i2i2−i2i2−i2i2−i2−2i2i00002i−2i00-220002−22−2−i2i2−i2i20000−22−2200000000
χ422-2-222-222-200-2−2i−2i2i2i00000i2−i2i2−i2i2−i2i2−i2−2i2i0000−2i2i002-2000−22−22i2−i2i2−i20000−22−2200000000
χ432-2-222-222-200-2−2i−2i2i2i00000−i2i2−i2i2−i2i2−i2i2−2i2i00002i−2i00-22000−22−22i2−i2i2−i200002−22−200000000
χ442-2-222-222-200-2−2i−2i2i2i00000−i2i2−i2i2−i2i2−i2i2−2i2i0000−2i2i002-20002−22−2−i2i2−i2i200002−22−200000000
χ452-2-22-222-2200-22i2i−2i−2i00000i2−i2−i2i2i2−i2−i2i2−2i2i2-200002i−2i00000i2−i2−i2i2−222−200002−2−2200000000
χ462-2-22-222-2200-22i2i−2i−2i00000i2−i2−i2i2i2−i2−i2i2−2i2i-220000−2i2i00000−i2i2i2−i22−2−2200002−2−2200000000
χ472-2-22-222-2200-22i2i−2i−2i00000−i2i2i2−i2−i2i2i2−i2−2i2i2-200002i−2i00000−i2i2i2−i22−2−220000−222−200000000
χ482-2-22-222-2200-22i2i−2i−2i00000−i2i2i2−i2−i2i2i2−i2−2i2i-220000−2i2i00000i2−i2−i2i2−222−20000−222−200000000
χ492-2-22-222-2200-2−2i−2i2i2i00000i2−i2−i2i2i2−i2−i2i22i−2i2-20000−2i2i00000i2−i2−i2i22−2−220000−222−200000000
χ502-2-22-222-2200-2−2i−2i2i2i00000i2−i2−i2i2i2−i2−i2i22i−2i-2200002i−2i00000−i2i2i2−i2−222−20000−222−200000000
χ512-2-22-222-2200-2−2i−2i2i2i00000−i2i2i2−i2−i2i2i2−i22i−2i2-20000−2i2i00000−i2i2i2−i2−222−200002−2−2200000000
χ522-2-22-222-2200-2−2i−2i2i2i00000−i2i2i2−i2−i2i2i2−i22i−2i-2200002i−2i00000i2−i2−i2i22−2−2200002−2−2200000000
χ53444444-4-4-444-40000-44-40000000000000000000000000000000000000000000000000
χ544444-4-4-44444-400004-4-40000000000000000000000000000000000000000000000000
χ5544-4-4000004i−4i022−2222−220002i2−2i20000000000002-20000002i−2i0000000002ζ−2ζ2ζ3−2ζ3000000000000
χ5644-4-4000004i−4i022−2222−220002i2−2i2000000000000-22000000−2i2i000000000−2ζ2ζ−2ζ32ζ3000000000000
χ5744-4-4000004i−4i0−2222−2222000−2i22i20000000000002-20000002i−2i000000000−2ζ2ζ−2ζ32ζ3000000000000
χ5844-4-4000004i−4i0−2222−2222000−2i22i2000000000000-22000000−2i2i0000000002ζ−2ζ2ζ3−2ζ3000000000000
χ5944-4-400000−4i4i022−2222−22000−2i22i20000000000002-2000000−2i2i000000000−2ζ32ζ3−2ζ2ζ000000000000
χ6044-4-400000−4i4i022−2222−22000−2i22i2000000000000-220000002i−2i0000000002ζ3−2ζ32ζ−2ζ000000000000
χ6144-4-400000−4i4i0−2222−22220002i2−2i20000000000002-2000000−2i2i0000000002ζ3−2ζ32ζ−2ζ000000000000
χ6244-4-400000−4i4i0−2222−22220002i2−2i2000000000000-220000002i−2i000000000−2ζ32ζ3−2ζ2ζ000000000000
χ634-4-444-4-4-4400400000000022−2222−22−2222−2222000000000000000000000000000000000000000
χ644-4-444-4-4-44004000000000−2222−222222−2222−22000000000000000000000000000000000000000
χ654-4-44-44-44-400400000000022−22−2222−222222−22000000000000000000000000000000000000000
χ664-4-44-44-44-4004000000000−222222−2222−22−2222000000000000000000000000000000000000000
χ678-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000
χ688-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.