Finite Group Databasebeta

← Group #491721

Character table — Group #491721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222444444444444444448888888888888888888888816161616163232323232
order1222444488882244488881616161616161616222488888881616161616161616161616162448824448
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-111
χ511111111111111-1-11-1-11111111111-1111-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ611111111111111-1-11-1-11111111111-1-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-111111111-11-1-1-11-1-111
χ811111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1111111111-1111-111-1-1
χ9111111111111-1-1111-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1
χ10111111111111-1-1111-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11
χ11111111111111-1-1111-1-111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-11-1-1-1-111-11
χ12111111111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-111111-11111-1-11-1
χ13111111111111-1-1-1-11111111111111-111-11-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11
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
χ15111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-11-1-1-1-11111111111-1-1-1-1-11-111-11-11-1
χ16111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-11-11-1-11-11-11
χ1722222222-2-2-2-22222222-2-20000000020022-2-2-2-2-2-20000000000000000000000
χ1822222222-2-2-2-222-2-22-2-2-2-200000000-2002-2-2-222220000000000000000000000
χ1922222222-2-2-2-2-2-2222-2-2-2-200000000200-2-222-2-2220000000000000000000000
χ2022222222-2-2-2-2-2-2-2-2222-2-200000000-200-222222-2-20000000000000000000000
χ2122222-2-2200002222-222002222−2−2−2−2-200-2-200000022−2−222−2−222−2−20000000000
χ2222222-2-2200002222-22200−2−2−2−22222-200-2-2000000−2−222−2−222−2−2220000000000
χ2322222-2-22000022-2-2-2-2-2002222−2−2−2−2200-2200000022−2−2−2−222−2−2220000000000
χ2422222-2-22000022-2-2-2-2-200−2−2−2−22222200-22000000−2−22222−2−222−2−20000000000
χ2522222-2-220000-2-222-2-2-2002222−2−2−2−2-20022000000−2−22222−2−2−2−2220000000000
χ2622222-2-220000-2-222-2-2-200−2−2−2−22222-2002200000022−2−2−2−22222−2−20000000000
χ2722222-2-220000-2-2-2-2-222002222−2−2−2−22002-2000000−2−222−2−22222−2−20000000000
χ2822222-2-220000-2-2-2-2-22200−2−2−2−222222002-200000022−2−222−2−2−2−2220000000000
χ292222-222-222220000-200-2-222-2-222-2-2022000000000000000000002-2-20000000
χ302222-222-222220000-200-2-222-2-222-2-20-2-200000000000000000000-2220000000
χ312222-222-222220000-200-2-2-2-222-2-22202200000000000000000000-2-220000000
χ322222-222-222220000-200-2-2-2-222-2-2220-2-20000000000000000000022-20000000
χ332-22-2200-222−2−22-22i−2i02i−2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000002−2i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ342-22-2200-222−2−22-22i−2i02i−2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000002−2i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ352-22-2200-222−2−22-2−2i2i0−2i2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000002−2−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ362-22-2200-222−2−22-2−2i2i0−2i2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000002−2−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ372-22-2200-222−2−2-222i−2i0−2i2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000−22i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ382-22-2200-222−2−2-222i−2i0−2i2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000−22i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ392-22-2200-222−2−2-22−2i2i02i−2i2−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000−22−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ402-22-2200-222−2−2-22−2i2i02i−2i2−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000−22−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ412-22-2200-2−2−2222-22i−2i02i−2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000−22−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ422-22-2200-2−2−2222-22i−2i02i−2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000−22−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ432-22-2200-2−2−2222-2−2i2i0−2i2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000−22i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ442-22-2200-2−2−2222-2−2i2i0−2i2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000−22i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ452-22-2200-2−2−222-222i−2i0−2i2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000002−2−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ462-22-2200-2−2−222-222i−2i0−2i2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000002−2−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ472-22-2200-2−2−222-22−2i2i02i−2i−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000002−2i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ482-22-2200-2−2−222-22−2i2i02i−2i−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000002−2i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ494444-444-4-4-4-4-40000-4004400000000000000000000000000000000000000000
χ504444-4-4-4-400000000400002222−22−22−22−222222000000000000000000000000000000000
χ514444-4-4-4-40000000040000−22−2222222222−22−22000000000000000000000000000000000
χ524-44-4-40042222−22−220000000−22222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000
χ534-44-4-40042222−22−220000000−2222−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000
χ544-44-4-4004−22−222222000000022−222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000
χ554-44-4-4004−22−222222000000022−22−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000
χ564-4-440-4404-44-40000000000000000004-4000000000000000000000000000000
χ574-4-440-4404-44-4000000000000000000-44000000000000000000000000000000
χ584-4-440-440-44-44000000000000000000000000000000000000000000022−2200000
χ594-4-440-440-44-440000000000000000000000000000000000000000000−222200000
χ6088-8-8000042−42−424200000000000000000000000000000000000000000000000000
χ6188-8-80000−424242−4200000000000000000000000000000000000000000000000000
χ628-8-8808-80000000000000000000000000000000000000000000000000000000

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