Finite Group Databasebeta

← Group #10696483

Character table — Group #10696483

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111112222222244444444448888888888888888161616161616161616161616242424242424242448484848
order122222223666666644444412121212888812121212242424242424242444441212121212121212888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1
χ922222222222222222-2-22-2-222220000-2-2-2-2000000002-20022-2-20000000000000000
χ1022222222222222222-2-22-2-222220000-2-2-2-200000000-2200-2-2220000000000000000
χ112222222222222222-22-2-22-2-2-2-2-2000022-2-2000000000000000000000000000020-20
χ122222222222222222-22-2-22-2-2-2-2-2000022-2-20000000000000000000000000000-2020
χ132222222222222222-2-22-2-22-2-2-2-20000-2-2220000000000000000000000000000020-2
χ142222222222222222-2-22-2-22-2-2-2-20000-2-22200000000000000000000000000000-202
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ1922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i32-200-1-111−i3−i3i3i3000000000000
χ2022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3-220011-1-1i3i3−i3−i3000000000000
χ2122222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i32-200-1-111i3i3−i3−i3000000000000
χ2222222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i3000000000000
χ232-2-22-2-2222-2-222-2-22222-2-2-222-2-22i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ242-2-22-2-2222-2-222-2-22222-2-2-222-2-2−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ252-2-22-2-2222-2-222-2-222-2-2-22222-2-20000-22-2200000000002-200002-22-2000000000000
χ262-2-22-2-2222-2-222-2-222-2-2-22222-2-20000-22-220000000000-220000-22-22000000000000
χ272-2-22-2-2222-2-222-2-22-22-22-22-2-22200002-2-220000000000000000000022-2-200000000
χ282-2-22-2-2222-2-222-2-22-22-22-22-2-22200002-2-2200000000000000000000-2-22200000000
χ292-2-22-2-2222-2-222-2-22-2-2222-2-2-2220000-222-200000000000000000000000022-2-20000
χ302-2-22-2-2222-2-222-2-22-2-2222-2-2-2220000-222-2000000000000000000000000-2-2220000
χ312-2-22-2-222-111-1-111-1222-2-2-2-1-1112i2i−2i−2i-11-11−i−iii−i−iii00003−33−3−i3i3i3−i3000000000000
χ322-2-22-2-222-111-1-111-1222-2-2-2-1-1112i2i−2i−2i-11-11−i−iii−i−iii0000−33−33i3−i3−i3i3000000000000
χ332-2-22-2-222-111-1-111-1222-2-2-2-1-111−2i−2i2i2i-11-11ii−i−iii−i−i00003−33−3i3−i3−i3i3000000000000
χ342-2-22-2-222-111-1-111-1222-2-2-2-1-111−2i−2i2i2i-11-11ii−i−iii−i−i0000−33−33−i3i3i3−i3000000000000
χ352-2-22-2-222-111-1-111-12-2-2-222-1-11100001-11-133−3−3−3−333002-23−3−33-11-11000000000000
χ362-2-22-2-222-111-1-111-12-2-2-222-1-11100001-11-133−3−3−3−33300-22−333−31-11-1000000000000
χ372-2-22-2-222-111-1-111-12-2-2-222-1-11100001-11-1−3−33333−3−3002-2−333−3-11-11000000000000
χ382-2-22-2-222-111-1-111-12-2-2-222-1-11100001-11-1−3−33333−3−300-223−3−331-11-1000000000000
χ3944444444-2-2-2-2-2-2-2-2-44-4-44-422220000-2-22200000000000000000000000000000000
χ4044444444-2-2-2-2-2-2-2-2-4-44-4-442222000022-2-200000000000000000000000000000000
χ414444-4-4-4-44444-4-4-4-400000000002-22-200002-22-22-22-2000000000000000000000000
χ424444-4-4-4-44444-4-4-4-40000000000-22-220000-22-22-22-22000000000000000000000000
χ434444-4-4-4-4-2-2-2-22222000000−2i32i3−2i32i32-22-20000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000
χ444444-4-4-4-4-2-2-2-22222000000−2i32i3−2i32i3-22-2200001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000
χ454444-4-4-4-4-2-2-2-222220000002i3−2i32i3−2i32-22-20000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000
χ464444-4-4-4-4-2-2-2-222220000002i3−2i32i3−2i3-22-2200001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000
χ4744-4-44-44-444-4-444-4-40000000000000000000000000000000000000000002i−2i2i−2i0000
χ4844-4-44-44-444-4-444-4-4000000000000000000000000000000000000000000−2i2i−2i2i0000
χ4944-4-4-44-4444-4-4-4-444000000000000000000000000000000000000002-22-200000000
χ5044-4-4-44-4444-4-4-4-44400000000000000000000000000000000000000-22-2200000000
χ514-44-44-4-444-44-4-44-44000000000000000000000000000000000000002-2-2200000000
χ524-44-44-4-444-44-4-44-4400000000000000000000000000000000000000-222-200000000
χ534-44-4-444-44-44-44-44-40000000000000000000000000000000000000000002i−2i−2i2i0000
χ544-44-4-444-44-44-44-44-4000000000000000000000000000000000000000000−2i2i2i−2i0000
χ554-4-4444-4-44-4-44-444-400000000002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ564-4-4444-4-44-4-44-444-40000000000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ574-4-4444-4-4-222-22-2-22000000−2i32i32i3−2i32i−2i−2i2i00002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7000000000000000000000000
χ584-4-4444-4-4-222-22-2-22000000−2i32i32i3−2i3−2i2i2i−2i0000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7000000000000000000000000
χ594-4-4444-4-4-222-22-2-220000002i3−2i3−2i32i32i−2i−2i2i00002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11000000000000000000000000
χ604-4-4444-4-4-222-22-2-220000002i3−2i3−2i32i3−2i2i2i−2i0000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11000000000000000000000000
χ614-4-44-4-444-222-2-222-2-44-44-4422-2-20000-222-200000000000000000000000000000000
χ624-4-44-4-444-222-2-222-2-4-4444-422-2-200002-2-2200000000000000000000000000000000
χ6388-8-88-88-8-4-444-4-44400000000000000000000000000000000000000000000000000
χ6488-8-8-88-88-4-44444-4-400000000000000000000000000000000000000000000000000
χ658-88-88-8-88-44-444-44-400000000000000000000000000000000000000000000000000
χ668-88-8-888-8-44-44-44-4400000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.