Finite Group Databasebeta

← Group #497413

Character table — Group #497413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222222244448888888822444444448888161616161616161616161616161616162222444488881616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1011111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1
χ1111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-1-111
χ1311111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ1411111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111
χ1511111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111
χ1611111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1
χ171-1-11-111-111-1-1-1-1111111-1-1-1-11-11-11-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1-11-1ii−i−iii−i−i1-1i−i1-11-1i−ii−i
χ181-1-11-111-111-1-1-1-1111111-1-1-1-11-11-11-11-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii1-11-1ii−i−iii−i−i-11−ii-11-11−ii−ii
χ191-1-11-111-111-1-1-1-1111111-1-1-1-11-11-11-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1-11-1−i−iii−i−iii1-1−ii1-11-1−ii−ii
χ201-1-11-111-111-1-1-1-1111111-1-1-1-11-11-11-11-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i1-11-1−i−iii−i−iii-11i−i-11-11i−ii−i
χ211-1-11-111-111-1-1-1-1111111-1-1-1-1-11-11-111-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i-11-11−i−iii−i−iii1-1−ii-11-11i−i−ii
χ221-1-11-111-111-1-1-1-1111111-1-1-1-1-11-11-111-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-11-11−i−iii−i−iii-11i−i1-11-1−iii−i
χ231-1-11-111-111-1-1-1-1111111-1-1-1-1-11-11-111-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii-11-11ii−i−iii−i−i1-1i−i-11-11−iii−i
χ241-1-11-111-111-1-1-1-1111111-1-1-1-1-11-11-111-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-11-11ii−i−iii−i−i-11−ii1-11-1i−i−ii
χ251-1-11-111-1-1-111-1-1111111-1-1-1-11-1-11-11-111-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-111-1−i−iiiii−i−i-11−ii-111-1−iii−i
χ261-1-11-111-1-1-111-1-1111111-1-1-1-11-1-11-11-111-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii-111-1−i−iiiii−i−i1-1i−i1-1-11i−i−ii
χ271-1-11-111-1-1-111-1-1111111-1-1-1-11-1-11-11-111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-111-1ii−i−i−i−iii-11i−i-111-1i−i−ii
χ281-1-11-111-1-1-111-1-1111111-1-1-1-11-1-11-11-111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i-111-1ii−i−i−i−iii1-1−ii1-1-11−iii−i
χ291-1-11-111-1-1-111-1-1111111-1-1-1-1-111-11-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i1-1-11ii−i−i−i−iii-11i−i1-1-11−ii−ii
χ301-1-11-111-1-1-111-1-1111111-1-1-1-1-111-11-1-11-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii1-1-11ii−i−i−i−iii1-1−ii-111-1i−ii−i
χ311-1-11-111-1-1-111-1-1111111-1-1-1-1-111-11-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii1-1-11−i−iiiii−i−i-11−ii1-1-11i−ii−i
χ321-1-11-111-1-1-111-1-1111111-1-1-1-1-111-11-1-11-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i1-1-11−i−iiiii−i−i1-1i−i-111-1−ii−ii
χ332222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000-2-2-2-200000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2000000000000000000000000222200000000000000000000
χ35222222222222-2-2-2-2000000002222-2-2-2-2-2-2000022−2−222−2−222−2−222−2−20000000000002−22−22−22−2000000000000
χ36222222222222-2-2-2-2000000002222-2-2-2-2-2-20000−2−222−2−222−2−222−2−222000000000000−22−22−22−22000000000000
χ37222222222222-2-2-2-200000000-2-2-2-222-2-222000022−2−222−2−222−2−222−2−2000000000000−22−22−22−22000000000000
χ38222222222222-2-2-2-200000000-2-2-2-222-2-2220000−2−222−2−222−2−222−2−2220000000000002−22−22−22−2000000000000
χ3922222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-222222200000000000000000000000022-2-200000000000000000000
χ4022222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000-2-22200000000000000000000
χ4122222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000022−2−222−2−2−2−222−2−222000000000000−22−222−22−2000000000000
χ4222222222-2-2-2-2-2-2-2-20000000022-2-22222-2-20000−2−222−2−22222−2−222−2−20000000000002−22−2−22−22000000000000
χ4322222222-2-2-2-2-2-2-2-200000000-2-222-2-22222000022−2−222−2−2−2−222−2−2220000000000002−22−2−22−22000000000000
χ4422222222-2-2-2-2-2-2-2-200000000-2-222-2-222220000−2−222−2−22222−2−222−2−2000000000000−22−222−22−2000000000000
χ4522-2-22-22-200002-2-2222-2-222-2-2000000000000002i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000000000000000
χ4622-2-22-22-200002-2-2222-2-222-2-2000000000000002i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000000000000000000000
χ4722-2-22-22-200002-2-2222-2-222-2-200000000000000−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000
χ4822-2-22-22-200002-2-2222-2-222-2-200000000000000−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000000000000000000000
χ492-22-2-2-2220000-22-2222-2-2-2-222000000000000002-22-2-22-22000000002-2-222-2-22000000000000000000000000
χ502-22-2-2-2220000-22-2222-2-2-2-222000000000000002-22-2-22-2200000000-222-2-222-2000000000000000000000000
χ512-22-2-2-2220000-22-2222-2-2-2-22200000000000000-22-222-22-2000000002-2-22-222-2000000000000000000000000
χ522-22-2-2-2220000-22-2222-2-2-2-22200000000000000-22-222-22-200000000-222-22-2-22000000000000000000000000
χ532-2-22-222-222-2-222-2-2000000002-22-2-22-22-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ542-2-22-222-222-2-222-2-2000000002-22-2-22-22-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ552-2-22-222-222-2-222-2-200000000-22-222-2-222-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ562-2-22-222-222-2-222-2-200000000-22-222-2-222-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ572-2-22-222-222-2-2-2-222-2-2-2-222222-22-22-22-22-2-2-222000000000000000000000000-22-2200000000000000000000
χ582-2-22-222-222-2-2-2-222-2-2-2-22222-22-22-222-2-22-2-2220000000000000000000000002-22-200000000000000000000
χ592-2-22-222-2-2-22222-2-2000000002-2-222-22-2-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ602-2-22-222-2-2-22222-2-2000000002-2-222-22-2-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ612-2-22-222-2-2-22222-2-200000000-222-2-222-22-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ622-2-22-222-2-2-22222-2-200000000-222-2-222-22-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ632-2-22-222-2-2-222-2-222-2-2-2-222222-2-22-22-222-222-2-20000000000000000000000002-2-2200000000000000000000
χ642-2-22-222-2-2-222-2-222-2-2-2-22222-222-22-2-22-2222-2-2000000000000000000000000-222-200000000000000000000
χ654444-4-4-4-44-44-4000022−2222−2222−2222−22000000000022−2222−22000000000000000000000000000000000000000000000000
χ664444-4-4-4-44-44-40000−2222−2222−2222−22220000000000−2222−2222000000000000000000000000000000000000000000000000
χ674444-4-4-4-4-44-44000022−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ684444-4-4-4-4-44-440000−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6944-4-44-44-400004-4-44-4-444-4-44400000000000000000000000000000000000000000000000000000000000000
χ7044-4-44-44-40000-444-400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000
χ7144-4-44-44-40000-444-40000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000
χ7244-4-4-44-440000000022−22−222222−22−222200000000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ7344-4-4-44-440000000022−22−222222−22−22220000000000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ7444-4-4-44-4400000000−222222−22−222222−2200000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ7544-4-4-44-4400000000−222222−22−222222−220000000000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ764-44-444-4-40000000022−22−2222−222222−2200000000000000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ774-44-444-4-40000000022−22−2222−222222−220000000000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ784-44-444-4-400000000−222222−2222−22−222200000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ794-44-444-4-400000000−222222−2222−22−22220000000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ804-44-4-4-44400004-44-4000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ814-44-4-4-44400004-44-40000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ824-44-4-4-4440000-44-44-4-44444-4-400000000000000000000000000000000000000000000000000000000000000
χ834-4-444-4-444-4-44000022−2222−22−2222−2222000000000022−22−2222000000000000000000000000000000000000000000000000
χ844-4-444-4-444-4-440000−2222−222222−2222−220000000000−222222−22000000000000000000000000000000000000000000000000
χ854-4-444-4-44-444-4000022−2222−22−2222−22220000000000−222222−22000000000000000000000000000000000000000000000000
χ864-4-444-4-44-444-40000−2222−222222−2222−22000000000022−22−2222000000000000000000000000000000000000000000000000

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