Finite Group Databasebeta

← Group #491913

Character table — Group #491913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222444444444444444448888888888888888888888816161616163232323232
order1222444488882244488881616161616161616244488888881616161616161616161616162248844448
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-11-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-111
χ511111111111111-1-11-1-11111111111-1111-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1
χ611111111111111-1-11-1-11111111111-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ711111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-11
χ811111111111111-1-11-1-111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-111111111-111111-1-11-1
χ9111111111111-1-1111-1-111111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1
χ10111111111111-1-1111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1111
χ11111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-111-1-1-111-1-11111-1-1-1-111111-1-1-1-11-1-111
χ12111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-11111-111-1-1
χ13111111111111-1-1-1-11111111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11
χ14111111111111-1-1-1-11111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1
χ15111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-11-1-111-11-11-1
χ16111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-111-1-11-11-11
χ1722222222-2-2-2-22222222-2-20000000022002-2-2-2-2-2-20000000000000000000000
χ1822222222-2-2-2-222-2-22-2-2-2-200000000-2200-2-2-222220000000000000000000000
χ1922222222-2-2-2-2-2-2222-2-2-2-2000000002-200-222-2-2220000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2222-2-200000000-2-20022222-2-20000000000000000000000
χ2122222-22-222220000-200-2-22222-2-2-2-200220000000000000000000-22-20000000
χ2222222-22-222220000-200-2-22222-2-2-2-200-2-200000000000000000002-220000000
χ2322222-22-222220000-200-2-2-2-2-2-2222200220000000000000000000-2-220000000
χ2422222-22-222220000-200-2-2-2-2-2-2222200-2-2000000000000000000022-20000000
χ252222-22-2200002222-2220022−2−222−2−2-2-200-200000022−2−222−2−222−2−20000000000
χ262222-22-2200002222-22200−2−222−2−222-2-200-2000000−2−222−2−222−2−2220000000000
χ272222-22-22000022-2-2-2-2-20022−2−222−2−22-200200000022−2−2−2−222−2−2220000000000
χ282222-22-22000022-2-2-2-2-200−2−222−2−2222-2002000000−2−22222−2−222−2−20000000000
χ292222-22-220000-2-222-2-2-20022−2−222−2−2-22002000000−2−22222−2−2−2−2220000000000
χ302222-22-220000-2-222-2-2-200−2−222−2−222-2200200000022−2−2−2−22222−2−20000000000
χ312222-22-220000-2-2-2-2-2220022−2−222−2−22200-2000000−2−222−2−22222−2−20000000000
χ322222-22-220000-2-2-2-2-22200−2−222−2−2222200-200000022−2−222−2−2−2−2220000000000
χ332-2-22020-222−2−22-22i−2i02i−2i2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000002−2i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ342-2-22020-222−2−22-22i−2i02i−2i2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000002−2i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ352-2-22020-222−2−22-2−2i2i0−2i2i2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000002−2−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ362-2-22020-222−2−22-2−2i2i0−2i2i2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000002−2−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ372-2-22020-222−2−2-222i−2i0−2i2i2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000−22i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ382-2-22020-222−2−2-222i−2i0−2i2i2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000−22i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ392-2-22020-222−2−2-22−2i2i02i−2i2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000−22−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ402-2-22020-222−2−2-22−2i2i02i−2i2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000−22−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ412-2-22020-2−2−2222-22i−2i02i−2i−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000−22−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ422-2-22020-2−2−2222-22i−2i02i−2i−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000−22−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ432-2-22020-2−2−2222-2−2i2i0−2i2i−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000−22i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ442-2-22020-2−2−2222-2−2i2i0−2i2i−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000−22i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ452-2-22020-2−2−222-222i−2i0−2i2i−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000002−2−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ462-2-22020-2−2−222-222i−2i0−2i2i−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000002−2−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ472-2-22020-2−2−222-22−2i2i02i−2i−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000002−2i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ482-2-22020-2−2−222-22−2i2i02i−2i−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000002−2i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ4944444-44-4-4-4-4-40000-4004400000000000000000000000000000000000000000
χ504444-4-4-4-400000000400002222−22−22−22−222222000000000000000000000000000000000
χ514444-4-4-4-40000000040000−22−2222222222−22−22000000000000000000000000000000000
χ524-44-4-40404-44-400000000000000000000000000000000000000000002i2−2i200000
χ534-44-4-40404-44-40000000000000000000000000000000000000000000−2i22i200000
χ544-44-4-4040-44-4400000000000000000004i−4i00000000000000000000000000000
χ554-44-4-4040-44-440000000000000000000−4i4i00000000000000000000000000000
χ564-4-440-4042222−22−220000000−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000
χ574-4-440-4042222−22−220000000−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000
χ584-4-440-404−22−222222000000022−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000
χ594-4-440-404−22−222222000000022−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000
χ6088-8-8000042−42−424200000000000000000000000000000000000000000000000000
χ6188-8-80000−424242−4200000000000000000000000000000000000000000000000000
χ628-88-880-80000000000000000000000000000000000000000000000000000000

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