Finite Group Databasebeta

← Group #138581

Character table — Group #138581

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12224444224444448888888844888816161616161616161616161616161616224488881616161616161616888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ1922222222222-2-2-2-2222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ2022222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ2122222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-22222-200000000-2-2000022−2−222−2−222−2−222−2−22-2-2200002−22−22−22−2000000000000
χ2422222222-2-2-22222-200000000-2-2000022−2−222−2−222−2−222−2−2-222-20000−22−22−22−22000000000000
χ2522222222-2-2-22222-200000000-2-20000−2−222−2−222−2−222−2−2222-2-220000−22−22−22−22000000000000
χ2622222222-2-2-22222-200000000-2-20000−2−222−2−222−2−222−2−222-222-200002−22−22−22−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ2922222222-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ3022222222-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-2-2-222-222-2-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i222-2-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ322222-2-2-2-222-222-2-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2-2220000−i2i2−i2i2i2−i2i2−i2000000000000
χ332222-2-2-2-222-222-2-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i222-2-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ342222-2-2-2-222-222-2-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2-2220000i2−i2i2−i2−i2i2−i2i2000000000000
χ352222-2-2-2-222-2-2-222-2000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002i−2i−2i2i−222−22−2−22000000000000
χ362222-2-2-2-222-2-2-222-2000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000−2i2i2i−2i2−2−22−222−2000000000000
χ372222-2-2-2-222-2-2-222-2000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002i−2i−2i2i2−2−22−222−2000000000000
χ382222-2-2-2-222-2-2-222-2000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000−2i2i2i−2i−222−22−2−22000000000000
χ392222-2-2-2-2-2-2222-2-22-2-2-2-222222-2-2-22200000000000000002-22-2-2-22200000000000000000000
χ402222-2-2-2-2-2-2222-2-22-2-2-2-222222-2-2-2220000000000000000-22-2222-2-200000000000000000000
χ412222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ422222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ432222-2-2-2-2-2-22-2-2222-2-2-2-22222-2222-2-200000000000000000000000022-2-2-2-222000000000000
χ442222-2-2-2-2-2-22-2-2222-2-2-2-22222-2222-2-2000000000000000000000000-2-22222-2-2000000000000
χ4522-2-222-2-22-2-20000222-2-2-2-222000000000000002-22-22-22-20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ4622-2-222-2-22-2-20000222-2-2-2-222000000000000002-22-22-22-20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ4722-2-222-2-22-2-20000222-2-2-2-22200000000000000-22-22-22-220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ4822-2-222-2-22-2-20000222-2-2-2-22200000000000000-22-22-22-220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ4922-2-2-2-222-22-20000222-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000i2−i2−i2i2−222−20000
χ5022-2-2-2-222-22-20000222-2-222-2-2000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000−i2i2i2−i22−2−220000
χ5122-2-2-2-222-22-20000222-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000i2−i2−i2i22−2−220000
χ5222-2-2-2-222-22-20000222-2-222-2-200000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000−i2i2i2−i2−222−20000
χ5344-4-444-4-44-4-400004-4-44444-4-400000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-4440000-4000000000000000000000022−22−222222−22−22220000000000000000000000000000
χ5544-4-444-4-4-4440000-40000000000000000000000−222222−22−222222−220000000000000000000000000000
χ5644-4-4-4-4444-440000-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ5744-4-4-4-4444-440000-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ5844-4-4-4-444-44-400004-4-444-4-44400000000000000000000000000000000000000000000000000
χ594-44-44i−4i4i−4i0000000022−2222−222i2−2i22i2−2i20000002ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3000000000000000000000000000000000000
χ604-44-44i−4i4i−4i0000000022−2222−222i2−2i22i2−2i2000000−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3000000000000000000000000000000000000
χ614-44-44i−4i4i−4i00000000−2222−2222−2i22i2−2i22i20000002ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000
χ624-44-44i−4i4i−4i00000000−2222−2222−2i22i2−2i22i2000000−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000
χ634-44-4−4i4i−4i4i0000000022−2222−22−2i22i2−2i22i20000002ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000
χ644-44-4−4i4i−4i4i0000000022−2222−22−2i22i2−2i22i2000000−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000
χ654-44-4−4i4i−4i4i00000000−2222−22222i2−2i22i2−2i20000002ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3000000000000000000000000000000000000
χ664-44-4−4i4i−4i4i00000000−2222−22222i2−2i22i2−2i2000000−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3000000000000000000000000000000000000
χ674-4-444i−4i−4i4i0004-44i−4i022−22−2222−2i22i22i2−2i20022−222i2−2i200000000000000000000000000000000000000000000
χ684-4-444i−4i−4i4i0004-44i−4i0−222222−222i2−2i2−2i22i200−2222−2i22i200000000000000000000000000000000000000000000
χ694-4-444i−4i−4i4i000-44−4i4i022−22−2222−2i22i22i2−2i200−2222−2i22i200000000000000000000000000000000000000000000
χ704-4-444i−4i−4i4i000-44−4i4i0−222222−222i2−2i2−2i22i20022−222i2−2i200000000000000000000000000000000000000000000
χ714-4-44−4i4i4i−4i0004-4−4i4i022−22−22222i2−2i2−2i22i20022−22−2i22i200000000000000000000000000000000000000000000
χ724-4-44−4i4i4i−4i0004-4−4i4i0−222222−22−2i22i22i2−2i200−22222i2−2i200000000000000000000000000000000000000000000
χ734-4-44−4i4i4i−4i000-444i−4i022−22−22222i2−2i2−2i22i200−22222i2−2i200000000000000000000000000000000000000000000
χ744-4-44−4i4i4i−4i000-444i−4i0−222222−22−2i22i22i2−2i20022−22−2i22i200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.