Finite Group Databasebeta

← Group #490777

Character table — Group #490777

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888844488888888882244888888161616161616161616161616161616162488882224
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-11
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-11
χ91111-1-1-1-111111111-1-1111-1-1-1-111-1-111111-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-11-11
χ101111-1-1-1-111111111-1-1111-1-1-1-111-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-11-1
χ111111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-111-1-1111-11-1
χ121111-1-1-1-111111111-1-1111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-11-11
χ131111-1-1-1-111111111-1-1111-1-1-1-1-1-1111111-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ141111-1-1-1-111111111-1-1111-1-1-1-1-1-1111111-11-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ151111-1-1-1-111111111-1-1111-1-1-1-1-1-111-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ161111-1-1-1-111111111-1-1111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ17222222222222-2-2-2-2222-2-2-2-2-2-22222000022-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-20000-2-2222200000000000000000000000000
χ1922222222-2-2220000-2-2-200000022220000-2-2000022−2−222−2−222−2−222−2−20000000000
χ2022222222-2-2220000-2-2-200000022220000-2-20000−2−222−2−222−2−222−2−2220000000000
χ2122222222-2-2220000-2-2-2000000-2-2-2-2000022000022−2−222−2−2−2−222−2−2220000000000
χ2222222222-2-2220000-2-2-2000000-2-2-2-20000220000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-222-2-222222-2-2-2-222-2-2000022-2-200000000000000000000002-200000000
χ24222222-2-222-2-222222-2-2-2-222-2-20000-2-2220000000000000000000000-2200000000
χ25222222-2-222-2-2-2-2-2-22-2-222-2-222000000000000000000000000000000002i−2i2i−2i0000
χ26222222-2-222-2-2-2-2-2-22-2-222-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ272222-2-22222-2-22222-22-2-2-2-2-222000022-2-20000000000000000000000-2200000000
χ282222-2-22222-2-22222-22-2-2-2-2-2220000-2-22200000000000000000000002-200000000
χ292222-2-22222-2-2-2-2-2-2-22-22222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ302222-2-22222-2-2-2-2-2-2-22-22222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ312222-2-2-2-22222-2-2-2-2-2-22-2-2222222-2-200002-2-2-22200000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-22-2-22222-2-2220000-2222-2-200000000000000000000000000
χ332222-2-2-2-2-2-222000022-200000022-2-20000-22000022−2−2−2−22222−2−2−2−2220000000000
χ342222-2-2-2-2-2-222000022-200000022-2-20000-220000−2−22222−2−2−2−22222−2−20000000000
χ352222-2-2-2-2-2-222000022-2000000-2-22200002-2000022−2−2−2−222−2−22222−2−20000000000
χ362222-2-2-2-2-2-222000022-2000000-2-22200002-20000−2−22222−2−222−2−2−2−2220000000000
χ372-2-222-22-200-222−22−20002−22−22−22-22-20000002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ382-2-222-22-200-222−22−20002−22−22−22-22-20000002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ392-2-222-22-200-222−22−20002−22−22−2-22-22000000−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ402-2-222-22-200-222−22−20002−22−22−2-22-22000000−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ412-2-222-22-200-22−22−22000−22−22−222-22-2000000−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ422-2-222-22-200-22−22−22000−22−22−222-22-2000000−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ432-2-222-22-200-22−22−22000−22−22−22-22-220000002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ442-2-222-22-200-22−22−22000−22−22−22-22-220000002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ452-2-22-22-2200-222−22−20002−2−22−222-2-220000002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ462-2-22-22-2200-222−22−20002−2−22−222-2-220000002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ472-2-22-22-2200-222−22−20002−2−22−22-222-2000000−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ482-2-22-22-2200-222−22−20002−2−22−22-222-2000000−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ492-2-22-22-2200-22−22−22000−222−22−22-2-22000000−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ502-2-22-22-2200-22−22−22000−222−22−22-2-22000000−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ512-2-22-22-2200-22−22−22000−222−22−2-222-20000002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ522-2-22-22-2200-22−22−22000−222−22−2-222-20000002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ53444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-400004-440000000000000000000000000000000000000000000000
χ5544-4-400004-40044-4-40000000000000004i−4i00000000000000000000000000000000
χ5644-4-400004-40044-4-4000000000000000−4i4i00000000000000000000000000000000
χ5744-4-400004-400-4-44400000000000004-40000000000000000000000000000000000
χ5844-4-400004-400-4-4440000000000000-440000000000000000000000000000000000
χ594-4-444-4-44004-422−2222−22000−222222−22−22220000000000000000000000000000000000000000
χ604-4-444-4-44004-4−2222−222200022−22−222222−220000000000000000000000000000000000000000
χ614-4-44-444-4004-422−2222−22000−2222−222222−220000000000000000000000000000000000000000
χ624-4-44-444-4004-4−2222−222200022−2222−22−22220000000000000000000000000000000000000000
χ6388-8-80000-880000000000000000000000000000000000000000000000000000000
χ648-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ658-88-800000000−424242−420000000000000000000000000000000000000000000000000

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