Finite Group Databasebeta

← Group #69494

Character table — Group #69494

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222222222222222224444444444444444444444444444444444121212121212121224242424
order12224444223444444666666612121212121212124444444444121212121212121212121212121212121212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-1-1-1-1-1111-1-111-1-1111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ141111-1-1-1-1-1-1111-1-111-1-1111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ151111-1-1-1-1-1-1111-1-111-1-1111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ161111-1-1-1-1-1-1111-1-111-1-1111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ172222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ192222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ202222222222-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ2122222222-2-22-2-22222-2-2222-2-2-2-2-2-22222-2-20000000022-2-222-2-20000000000000000000000000000
χ2222222222-2-22-2-2-2-2-2-2-2-2222-2-2-2-2-2-222222200000000-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-1-2-2222211-1-1-1111111-1-1-1-1-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−3000000000000
χ2422222222-2-2-1-2-2222211-1-1-1111111-1-1-1-1-2-200000000-1-111-1-111−3−333−3−333−3−333−3−333000000000000
χ2522222222-2-2-1-2-2-2-2-2-211-1-1-1111111-1-1-1-1220000000011-1-111-1-133−3−333−3−3−3−333−3−333000000000000
χ2622222222-2-2-1-2-2-2-2-2-211-1-1-1111111-1-1-1-1220000000011-1-111-1-1−3−333−3−33333−3−333−3−3000000000000
χ272222-2-2-2-2222-2-222-2-22222222-2-2-2-2-2-2-2-2-220000000022-2-2-2-2220000000000000000000000000000
χ282222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-200000000-2-22222-2-20000000000000000000000000000
χ292222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ302222-2-2-2-222-1-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ312222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ322222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ332222-2-2-2-2-2-2-12222-2-211-1-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ342222-2-2-2-2-2-2-12222-2-211-1-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ352222-2-2-2-2-2-2-122-2-22211-1-1-111-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ362222-2-2-2-2-2-2-122-2-22211-1-1-111-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-2-222-2-22-222-20000222-2-2-2-222-2-222-2-200000000000000000000000000000000002-22-200000000
χ3822-2-222-2-22-222-20000222-2-2-2-222-2-222-2-20000000000000000000000000000000000-22-2200000000
χ3922-2-222-2-2-222-220000-2-22-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ4022-2-222-2-2-222-220000-2-22-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ4122-2-2-2-2222-22-220000222-2-2-2-2-2-222-2-222000000000000000000000000000000000000002i−2i−2i2i0000
χ4222-2-2-2-2222-22-220000222-2-2-2-2-2-222-2-22200000000000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-2-2-222-2222-20000-2-22-2-22222-2-2-2-22200000000000000000000000000000000002-2-2200000000
χ4422-2-2-2-222-2222-20000-2-22-2-22222-2-2-2-2220000000000000000000000000000000000-222-200000000
χ452-22-22i−2i2i−2i002002-22i−2i00-22-20000002i−2i2i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i2-2002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ462-22-22i−2i2i−2i002002-22i−2i00-22-20000002i−2i2i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i2-2002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ472-22-22i−2i2i−2i00200-22−2i2i00-22-20000002i−2i2i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i-2200−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ482-22-22i−2i2i−2i00200-22−2i2i00-22-20000002i−2i2i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i-2200−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ492-22-22i−2i2i−2i00-1002-22i−2i−i3i31-11−i3i33−33−3−ii−ii001+i−1−i1−i−1+i1+i−1−i1−i−1+i-113−3−ii−i3i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ502-22-22i−2i2i−2i00-1002-22i−2i−i3i31-11−i3i33−33−3−ii−ii00−1−i1+i−1+i1−i−1−i1+i−1+i1−i-113−3−ii−i3i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ512-22-22i−2i2i−2i00-1002-22i−2ii3−i31-11i3−i3−33−33−ii−ii001+i−1−i1−i−1+i1+i−1−i1−i−1+i-11−33−iii3−i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ522-22-22i−2i2i−2i00-1002-22i−2ii3−i31-11i3−i3−33−33−ii−ii00−1−i1+i−1+i1−i−1−i1+i−1+i1−i-11−33−iii3−i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ532-22-22i−2i2i−2i00-100-22−2i2i−i3i31-11−i3i33−33−3−ii−ii001+i−1−i1−i−1+i−1−i1+i−1+i1−i1-1−33i−ii3−i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ542-22-22i−2i2i−2i00-100-22−2i2i−i3i31-11−i3i33−33−3−ii−ii00−1−i1+i−1+i1−i1+i−1−i1−i−1+i1-1−33i−ii3−i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ552-22-22i−2i2i−2i00-100-22−2i2ii3−i31-11i3−i3−33−33−ii−ii001+i−1−i1−i−1+i−1−i1+i−1+i1−i1-13−3i−i−i3i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ562-22-22i−2i2i−2i00-100-22−2i2ii3−i31-11i3−i3−33−33−ii−ii00−1−i1+i−1+i1−i1+i−1−i1−i−1+i1-13−3i−i−i3i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ572-22-2−2i2i−2i2i002002-2−2i2i00-22-2000000−2i2i−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i2-200−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ582-22-2−2i2i−2i2i002002-2−2i2i00-22-2000000−2i2i−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i2-200−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ592-22-2−2i2i−2i2i00200-222i−2i00-22-2000000−2i2i−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i-22002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ602-22-2−2i2i−2i2i00200-222i−2i00-22-2000000−2i2i−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i-22002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ612-22-2−2i2i−2i2i00-1002-2−2i2i−i3i31-11−i3i3−33−33i−ii−i001−i−1+i1+i−1−i1−i−1+i1+i−1−i-11−33i−i−i3i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ622-22-2−2i2i−2i2i00-1002-2−2i2i−i3i31-11−i3i3−33−33i−ii−i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i-11−33i−i−i3i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ632-22-2−2i2i−2i2i00-1002-2−2i2ii3−i31-11i3−i33−33−3i−ii−i001−i−1+i1+i−1−i1−i−1+i1+i−1−i-113−3i−ii3−i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ642-22-2−2i2i−2i2i00-1002-2−2i2ii3−i31-11i3−i33−33−3i−ii−i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i-113−3i−ii3−i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ652-22-2−2i2i−2i2i00-100-222i−2i−i3i31-11−i3i3−33−33i−ii−i001−i−1+i1+i−1−i−1+i1−i−1−i1+i1-13−3−iii3−i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ662-22-2−2i2i−2i2i00-100-222i−2i−i3i31-11−i3i3−33−33i−ii−i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i1-13−3−iii3−i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ672-22-2−2i2i−2i2i00-100-222i−2ii3−i31-11i3−i33−33−3i−ii−i001−i−1+i1+i−1−i−1+i1−i−1−i1+i1-1−33−ii−i3i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ682-22-2−2i2i−2i2i00-100-222i−2ii3−i31-11i3−i33−33−3i−ii−i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i1-1−33−ii−i3i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ6944-4-444-4-44-4-24-40000-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000
χ7044-4-444-4-4-44-2-44000022-222-2-222-2-2-2-2220000000000000000000000000000000000000000000000
χ7144-4-4-4-4444-4-2-440000-2-2-2222222-2-222-2-20000000000000000000000000000000000000000000000
χ7244-4-4-4-444-44-24-4000022-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i00400000000-4-440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ744-4-444i−4i−4i4i00-2000000−2i32i322-22i3−2i323−23−2323−2i2i2i−2i0000000000000000000000000000000000000000000000
χ754-4-444i−4i−4i4i00-20000002i3−2i322-2−2i32i3−232323−23−2i2i2i−2i0000000000000000000000000000000000000000000000
χ764-4-44−4i4i4i−4i00400000000-4-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i00-2000000−2i32i322-22i3−2i3−232323−232i−2i−2i2i0000000000000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i00-20000002i3−2i322-2−2i32i323−23−23232i−2i−2i2i0000000000000000000000000000000000000000000000

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