Finite Group Databasebeta

← Group #69433

Character table — Group #69433

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order12222234444444466666661212121212121212444444444412121212121212121212121212121212121212121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-1-1111111ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-1-1111111ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-1-1111111−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-11-1-1-1-111-1-1111-1-1-1-1-1-1-1-1111111−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ17222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22-200000000-2-2-2-22222000000000000000000000000
χ182222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000
χ19222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ20222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000
χ21222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-2000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000
χ22222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-2000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000
χ23222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000
χ24222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000
χ25222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-222222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000
χ26222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-22-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000
χ272222-2-2222-2-22222222-2-2-2-2-2-2-2-22222-2-200000000-2-22222-2-2000000000000000000000000
χ282222-2-22-2-222-2-222222-2-2-2-22222-2-2-2-22-200000000-2-222-2-222000000000000000000000000
χ292222-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-222i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii00000000
χ302222-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-22−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i00000000
χ312222-2-2-122-2-22222-1-1-111111111-1-1-1-1-2-20000000011-1-1-1-11133−3−3−3−33333−3−3−3−33300000000
χ322222-2-2-122-2-22222-1-1-111111111-1-1-1-1-2-20000000011-1-1-1-111−3−33333−3−3−3−33333−3−300000000
χ332222-2-2-1-2-222-2-222-1-1-11111-1-1-1-111112-20000000011-1-111-1-133−3−3−3−333−3−33333−3−300000000
χ342222-2-2-1-2-222-2-222-1-1-11111-1-1-1-111112-20000000011-1-111-1-1−3−33333−3−333−3−3−3−33300000000
χ352222-2-2-1-2-2-2-222-2-2-1-1-111111111-1-1-1-1222i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000
χ362222-2-2-1-2-2-2-222-2-2-1-1-111111111-1-1-1-122−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000
χ372-22-20022i−2i002-22i−2i2-2-20000000022-2-2001+i−1−i1−i−1+i1−i−1+i1+i−1−i002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ382-22-20022i−2i002-22i−2i2-2-20000000022-2-200−1−i1+i−1+i1−i−1+i1−i−1−i1+i002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ392-22-20022i−2i00-22−2i2i2-2-200000000-2-222001−i−1+i1+i−1−i−1−i1+i−1+i1−i00−2i2i2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ402-22-20022i−2i00-22−2i2i2-2-200000000-2-22200−1+i1−i−1−i1+i1+i−1−i1−i−1+i00−2i2i2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ412-22-2002−2i2i002-2−2i2i2-2-20000000022-2-2001−i−1+i1+i−1−i1+i−1−i1−i−1+i00−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ422-22-2002−2i2i002-2−2i2i2-2-20000000022-2-200−1+i1−i−1−i1+i−1−i1+i−1+i1−i00−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ432-22-2002−2i2i00-222i−2i2-2-200000000-2-222001+i−1−i1−i−1+i−1+i1−i−1−i1+i002i−2i−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ442-22-2002−2i2i00-222i−2i2-2-200000000-2-22200−1−i1+i−1+i1−i1−i−1+i1+i−1−i002i−2i−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ452-22-200-12i−2i002-22i−2i-111−i3−i3i3i3−i3−i3i3i3-1-111001+i−1−i1−i−1+i1−i−1+i1+i−1−i3−3−ii−ii3−3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ462-22-200-12i−2i002-22i−2i-111−i3−i3i3i3−i3−i3i3i3-1-11100−1−i1+i−1+i1−i−1+i1−i−1−i1+i3−3−ii−ii3−3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ472-22-200-12i−2i002-22i−2i-111i3i3−i3−i3i3i3−i3−i3-1-111001+i−1−i1−i−1+i1−i−1+i1+i−1−i−33−ii−ii−33−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ482-22-200-12i−2i002-22i−2i-111i3i3−i3−i3i3i3−i3−i3-1-11100−1−i1+i−1+i1−i−1+i1−i−1−i1+i−33−ii−ii−33ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ492-22-200-12i−2i00-22−2i2i-111−i3−i3i3i3i3i3−i3−i311-1-1001−i−1+i1+i−1−i−1−i1+i−1+i1−i−33i−i−ii3−3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ502-22-200-12i−2i00-22−2i2i-111−i3−i3i3i3i3i3−i3−i311-1-100−1+i1−i−1−i1+i1+i−1−i1−i−1+i−33i−i−ii3−3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ512-22-200-12i−2i00-22−2i2i-111i3i3−i3−i3−i3−i3i3i311-1-1001−i−1+i1+i−1−i−1−i1+i−1+i1−i3−3i−i−ii−33−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ522-22-200-12i−2i00-22−2i2i-111i3i3−i3−i3−i3−i3i3i311-1-100−1+i1−i−1−i1+i1+i−1−i1−i−1+i3−3i−i−ii−33ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ532-22-200-1−2i2i002-2−2i2i-111−i3−i3i3i3−i3−i3i3i3-1-111001−i−1+i1+i−1−i1+i−1−i1−i−1+i−33i−ii−i−33−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ542-22-200-1−2i2i002-2−2i2i-111−i3−i3i3i3−i3−i3i3i3-1-11100−1+i1−i−1−i1+i−1−i1+i−1+i1−i−33i−ii−i−33ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ552-22-200-1−2i2i002-2−2i2i-111i3i3−i3−i3i3i3−i3−i3-1-111001−i−1+i1+i−1−i1+i−1−i1−i−1+i3−3i−ii−i3−3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ562-22-200-1−2i2i002-2−2i2i-111i3i3−i3−i3i3i3−i3−i3-1-11100−1+i1−i−1−i1+i−1−i1+i−1+i1−i3−3i−ii−i3−3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ572-22-200-1−2i2i00-222i−2i-111−i3−i3i3i3i3i3−i3−i311-1-1001+i−1−i1−i−1+i−1+i1−i−1−i1+i3−3−iii−i−33−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ582-22-200-1−2i2i00-222i−2i-111−i3−i3i3i3i3i3−i3−i311-1-100−1−i1+i−1+i1−i1−i−1+i1+i−1−i3−3−iii−i−33ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ592-22-200-1−2i2i00-222i−2i-111i3i3−i3−i3−i3−i3i3i311-1-1001+i−1−i1−i−1+i−1+i1−i−1−i1+i−33−iii−i3−3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ602-22-200-1−2i2i00-222i−2i-111i3i3−i3−i3−i3−i3i3i311-1-100−1−i1+i−1+i1−i1−i−1+i1+i−1−i−33−iii−i3−3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ6144-4-44-4400000000-44-44-44-400000000000000000000000000000000000000000000000000
χ6244-4-44-4-2000000002-22-22-2223−2323−2323−2323−23000000000000000000000000000000000000000000
χ6344-4-44-4-2000000002-22-22-22−2323−2323−2323−2323000000000000000000000000000000000000000000
χ6444-4-4-44400000000-44-4-44-4400000000000000000000000000000000000000000000000000
χ6544-4-4-44-2000000002-222-22-223−2323−23−2323−2323000000000000000000000000000000000000000000
χ6644-4-4-44-2000000002-222-22-2−2323−232323−2323−23000000000000000000000000000000000000000000
χ674-4-44004004i−4i0000-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-4400400−4i4i0000-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-4400-2004i−4i000022-2−2i32i32i3−2i3−2i2i2i−2i23−23−2323000000000000000000000000000000000000000000
χ704-4-4400-2004i−4i000022-22i3−2i3−2i32i3−2i2i2i−2i−232323−23000000000000000000000000000000000000000000
χ714-4-4400-200−4i4i000022-2−2i32i32i3−2i32i−2i−2i2i−232323−23000000000000000000000000000000000000000000
χ724-4-4400-200−4i4i000022-22i3−2i3−2i32i32i−2i−2i2i23−23−2323000000000000000000000000000000000000000000

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