Finite Group Databasebeta

← Group #69801

Character table — Group #69801

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order12222234444444466666661212121212121212448888888812121212121212122424242424242424242424242424242444448888
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
χ5111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i
χ6111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii
χ7111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii
χ8111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i
χ91111-1-11-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-11-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-11-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-11-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-11
χ141111-1-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1
χ151111-1-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11-111-1
χ161111-1-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-11-1-11
χ172222222-2-22222-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2200000000-2-2-2-22222000000000000000000000000
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
χ21222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000
χ22222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000
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−i3i3i3−i3−i3i3i3−i3−i3i3i300000000
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−i3i3i3−i3−i3i3i3−i3−i300000000
χ25222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-22000000001111-1-1-1-133−3−333−3−3−3−333−3−33300000000
χ26222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-22000000001111-1-1-1-1−3−333−3−33333−3−333−3−300000000
χ272222-2-222222-2-222-2-2-2-22222222-2-2-2-2-2-200000000-2-222-2-222000000000000000000000000
χ282222-2-2222-2-222-2-2-2-2-2-2222-2-2-2-22222-2200000000-2-22222-2-2000000000000000000000000
χ292222-2-2-12222-2-2221111-1-1-1-1-1-1-11111-2-20000000011-1-111-1-133−3−3−3−33333−3−3−3−33300000000
χ302222-2-2-12222-2-2221111-1-1-1-1-1-1-11111-2-20000000011-1-111-1-1−3−33333−3−3−3−33333−3−300000000
χ312222-2-2-122-2-222-2-21111-1-1-11111-1-1-1-1-220000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000
χ322222-2-2-122-2-222-2-21111-1-1-11111-1-1-1-1-220000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000
χ332222-2-2-1-2-222-2-2-2-21111-1-1-1-1-1-1-11111222i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii00000000
χ342222-2-2-1-2-222-2-2-2-21111-1-1-1-1-1-1-1111122−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i00000000
χ352222-2-2-1-2-2-2-222221111-1-1-11111-1-1-1-12-222-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-100000000
χ362222-2-2-1-2-2-2-222221111-1-1-11111-1-1-1-12-2-2-22222-2-2-1-11111-1-11111-1-1-1-1-1-1-1-1111100000000
χ372-22-20022i−2i2-2002i−2i00002-2-222-2-20000001+i−1−i1−i−1+i1+i−1−i1−i−1+i002i−2i002i−2i1+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−2i2-2002i−2i00002-2-222-2-2000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i002i−2i002i−2i−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−2i-2200−2i2i00002-2-2-2-2220000001−i−1+i−1−i1+i−1+i1−i1+i−1−i002i−2i00−2i2i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i00000000
χ402-22-20022i−2i-2200−2i2i00002-2-2-2-222000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i002i−2i00−2i2i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i00000000
χ412-22-2002−2i2i2-200−2i2i00002-2-222-2-20000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00−2i2i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ422-22-2002−2i2i2-200−2i2i00002-2-222-2-2000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00−2i2i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ432-22-2002−2i2i-22002i−2i00002-2-2-2-2220000001+i−1−i−1+i1−i−1−i1+i1−i−1+i00−2i2i002i−2i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i00000000
χ442-22-2002−2i2i-22002i−2i00002-2-2-2-222000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i00−2i2i002i−2i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i00000000
χ452-22-200-12i−2i2-2002i−2i−i3−i3i3i3-111-1-111−i3−i3i3i3001+i−1−i1−i−1+i1+i−1−i1−i−1+i3−3−ii3−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ462-22-200-12i−2i2-2002i−2i−i3−i3i3i3-111-1-111−i3−i3i3i300−1−i1+i−1+i1−i−1−i1+i−1+i1−i3−3−ii3−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ472-22-200-12i−2i2-2002i−2ii3i3−i3−i3-111-1-111i3i3−i3−i3001+i−1−i1−i−1+i1+i−1−i1−i−1+i−33−ii−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ482-22-200-12i−2i2-2002i−2ii3i3−i3−i3-111-1-111i3i3−i3−i300−1−i1+i−1+i1−i−1−i1+i−1+i1−i−33−ii−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ492-22-200-12i−2i-2200−2i2i−i3−i3i3i3-11111-1-1i3i3−i3−i3001−i−1+i−1−i1+i−1+i1−i1+i−1−i3−3−ii−33i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ502-22-200-12i−2i-2200−2i2i−i3−i3i3i3-11111-1-1i3i3−i3−i300−1+i1−i1+i−1−i1−i−1+i−1−i1+i3−3−ii−33i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ512-22-200-12i−2i-2200−2i2ii3i3−i3−i3-11111-1-1−i3−i3i3i3001−i−1+i−1−i1+i−1+i1−i1+i−1−i−33−ii3−3i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ522-22-200-12i−2i-2200−2i2ii3i3−i3−i3-11111-1-1−i3−i3i3i300−1+i1−i1+i−1−i1−i−1+i−1−i1+i−33−ii3−3i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ532-22-200-1−2i2i2-200−2i2i−i3−i3i3i3-111-1-111−i3−i3i3i3001−i−1+i1+i−1−i1−i−1+i1+i−1−i−33i−i−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ542-22-200-1−2i2i2-200−2i2i−i3−i3i3i3-111-1-111−i3−i3i3i300−1+i1−i−1−i1+i−1+i1−i−1−i1+i−33i−i−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ552-22-200-1−2i2i2-200−2i2ii3i3−i3−i3-111-1-111i3i3−i3−i3001−i−1+i1+i−1−i1−i−1+i1+i−1−i3−3i−i3−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ562-22-200-1−2i2i2-200−2i2ii3i3−i3−i3-111-1-111i3i3−i3−i300−1+i1−i−1−i1+i−1+i1−i−1−i1+i3−3i−i3−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ572-22-200-1−2i2i-22002i−2i−i3−i3i3i3-11111-1-1i3i3−i3−i3001+i−1−i−1+i1−i−1−i1+i1−i−1+i−33i−i3−3−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ582-22-200-1−2i2i-22002i−2i−i3−i3i3i3-11111-1-1i3i3−i3−i300−1−i1+i1−i−1+i1+i−1−i−1+i1−i−33i−i3−3−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ592-22-200-1−2i2i-22002i−2ii3i3−i3−i3-11111-1-1−i3−i3i3i3001+i−1−i−1+i1−i−1−i1+i1−i−1+i3−3i−i−33−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ602-22-200-1−2i2i-22002i−2ii3i3−i3−i3-11111-1-1−i3−i3i3i300−1−i1+i1−i−1+i1+i−1−i−1+i1−i3−3i−i−33−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ6144-4-44-44000000004-44-4-44-400000000000000000000000000000000000000000000000000
χ6244-4-44-4-200000000-22-222-2223−2323−2323−2323−23000000000000000000000000000000000000000000
χ6344-4-44-4-200000000-22-222-22−2323−2323−2323−2323000000000000000000000000000000000000000000
χ6444-4-4-44400000000-44-44-44-400000000000000000000000000000000000000000000000000
χ6544-4-4-44-2000000002-22-22-2223−2323−23−2323−2323000000000000000000000000000000000000000000
χ6644-4-4-44-2000000002-22-22-22−2323−232323−2323−23000000000000000000000000000000000000000000
χ674-4-4400400004i−4i000000-4-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ684-4-440040000−4i4i000000-4-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ694-4-4400-200004i−4i00−2i32i32i3−2i322-223−23−2323−2i2i2i−2i000000000000000000000000000000000000000000
χ704-4-4400-200004i−4i002i3−2i3−2i32i322-2−232323−23−2i2i2i−2i000000000000000000000000000000000000000000
χ714-4-4400-20000−4i4i00−2i32i32i3−2i322-2−232323−232i−2i−2i2i000000000000000000000000000000000000000000
χ724-4-4400-20000−4i4i002i3−2i3−2i32i322-223−23−23232i−2i−2i2i000000000000000000000000000000000000000000

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