Finite Group Databasebeta

← Group #69445

Character table — Group #69445

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order1222222234444446666666121212121212121224444444446666121212121212121212121212121212121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111-1-1111-1-1-1-111-1-1-1-111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−i
χ6111111-1-1111-1-1-1-111-1-1-1-111111-1-1-1-1-11iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-111−i−iii
χ7111111-1-1111-1-1-1-111-1-1-1-111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii
χ8111111-1-1111-1-1-1-111-1-1-1-111111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-111ii−i−i
χ91111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-11-11-1
χ101111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11-11-11
χ111111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-1-11-11
χ121111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-111-11-1
χ131111-1-1-1-11-1-111-1-111-1-1-1-11-1-1-1-1111111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-11i−i−ii
χ141111-1-1-1-11-1-111-1-111-1-1-1-11-1-1-1-1111111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-111-1−iii−i
χ151111-1-1-1-11-1-111-1-111-1-1-1-11-1-1-1-1111111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-11−iii−i
χ161111-1-1-1-11-1-111-1-111-1-1-1-11-1-1-1-1111111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-111-1i−i−ii
χ17222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22-20000000022220000000000000000-2-2-2-200000000
χ1822222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1922222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-100000000
χ2022222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-200000000-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3111100000000
χ2122222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-200000000-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3111100000000
χ22222222-2-22-2-2222222-2-2-2-22-2-2-2-22222-2-20000000022-2-20000000000000000-2-22200000000
χ23222222-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-222i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-11100000000
χ24222222-2-2-122-2-2-2-2-1-11111-1-1-1-1-11111-22−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-11100000000
χ25222222-2-2-1-2-22222-1-11111-11111-1-1-1-1-2-200000000-1-11133−3−333−3−3−3−333−3−33311-1-100000000
χ26222222-2-2-1-2-22222-1-11111-11111-1-1-1-1-2-200000000-1-111−3−333−3−33333−3−333−3−311-1-100000000
χ272222-2-22222222-2-2222222222222222-2-200000000-2-2-2-20000000000000000-2-2-2-200000000
χ282222-2-222-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000001111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3111100000000
χ292222-2-222-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000001111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3111100000000
χ302222-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-2222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-100000000
χ312222-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-22-2-222-2-22211111111-1-1-1-11111-1-1-1-1-1-1-1-100000000
χ322222-2-2-2-2222-2-22222-2-2-2-222222-2-2-2-22-200000000-2-2220000000000000000-2-22200000000
χ332222-2-2-2-2-122-2-222-1-11111-1-1-1-1-111112-20000000011-1-133−3−3−3−333−3−33333−3−311-1-100000000
χ342222-2-2-2-2-122-2-222-1-11111-1-1-1-1-111112-20000000011-1-1−3−33333−3−333−3−3−3−33311-1-100000000
χ352222-2-2-2-2-1-2-222-2-2-1-11111-11111-1-1-1-1222i2i−2i−2i−2i−2i2i2i11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11100000000
χ362222-2-2-2-2-1-2-222-2-2-1-11111-11111-1-1-1-122−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11100000000
χ372-22-22-2002002i−2i2i−2i2-20000-200002i2i−2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i002i−2i00000000
χ382-22-22-2002002i−2i2i−2i2-20000-200002i2i−2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i002i−2i00000000
χ392-22-22-200200−2i2i−2i2i2-20000-20000−2i−2i2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00−2i2i00000000
χ402-22-22-200200−2i2i−2i2i2-20000-20000−2i−2i2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00−2i2i00000000
χ412-22-22-200-1002i−2i2i−2i-11−i3−i3i3i3133−3−3−i−iii001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11−i3i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ113−3−ii00000000
χ422-22-22-200-1002i−2i2i−2i-11−i3−i3i3i3133−3−3−i−iii00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11−i3i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ113−3−ii00000000
χ432-22-22-200-1002i−2i2i−2i-11i3i3−i3−i31−3−333−i−iii001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11i3−i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−33−ii00000000
χ442-22-22-200-1002i−2i2i−2i-11i3i3−i3−i31−3−333−i−iii00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11i3−i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−33−ii00000000
χ452-22-22-200-100−2i2i−2i2i-11−i3−i3i3i31−3−333ii−i−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11−i3i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−33i−i00000000
χ462-22-22-200-100−2i2i−2i2i-11−i3−i3i3i31−3−333ii−i−i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11−i3i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−33i−i00000000
χ472-22-22-200-100−2i2i−2i2i-11i3i3−i3−i3133−3−3ii−i−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11i3−i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ73−3i−i00000000
χ482-22-22-200-100−2i2i−2i2i-11i3i3−i3−i3133−3−3ii−i−i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11i3−i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ73−3i−i00000000
χ492-22-2-22002002i−2i−2i2i2-20000-200002i2i−2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i-22001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00−2i2i00000000
χ502-22-2-22002002i−2i−2i2i2-20000-200002i2i−2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00−2i2i00000000
χ512-22-2-2200200−2i2i2i−2i2-20000-20000−2i−2i2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i-22001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i002i−2i00000000
χ522-22-2-2200200−2i2i2i−2i2-20000-20000−2i−2i2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i002i−2i00000000
χ532-22-2-2200-1002i−2i−2i2i-11−i3−i3i3i3133−3−3−i−iii001−i−1+i−1+i1−i1+i−1−i−1−i1+i1-1i3−i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−33i−i00000000
χ542-22-2-2200-1002i−2i−2i2i-11−i3−i3i3i3133−3−3−i−iii00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1-1i3−i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−33i−i00000000
χ552-22-2-2200-1002i−2i−2i2i-11i3i3−i3−i31−3−333−i−iii001−i−1+i−1+i1−i1+i−1−i−1−i1+i1-1−i3i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ73−3i−i00000000
χ562-22-2-2200-1002i−2i−2i2i-11i3i3−i3−i31−3−333−i−iii00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1-1−i3i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ73−3i−i00000000
χ572-22-2-2200-100−2i2i2i−2i-11−i3−i3i3i31−3−333ii−i−i001+i−1−i−1−i1+i1−i−1+i−1+i1−i1-1i3−i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ113−3−ii00000000
χ582-22-2-2200-100−2i2i2i−2i-11−i3−i3i3i31−3−333ii−i−i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1-1i3−i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ113−3−ii00000000
χ592-22-2-2200-100−2i2i2i−2i-11i3i3−i3−i3133−3−3ii−i−i001+i−1−i−1−i1+i1−i−1+i−1+i1−i1-1−i3i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−33−ii00000000
χ602-22-2-2200-100−2i2i2i−2i-11i3i3−i3−i3133−3−3ii−i−i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1-1−i3i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−33−ii00000000
χ6144-4-4004-44000000-444-44-4-400000000000000000000000000000000000000000000000000
χ6244-4-4004-4-20000002-2-22-22223−2323−2323−2323−23000000000000000000000000000000000000000000
χ6344-4-4004-4-20000002-2-22-222−2323−2323−2323−2323000000000000000000000000000000000000000000
χ6444-4-400-444000000-44-44-44-400000000000000000000000000000000000000000000000000
χ6544-4-400-44-20000002-22-22-2223−2323−23−2323−2323000000000000000000000000000000000000000000
χ6644-4-400-44-20000002-22-22-22−2323−232323−2323−23000000000000000000000000000000000000000000
χ674-4-44000044-40000-4-4000044-4-440000000000000000000000000000000000000000000000
χ684-4-4400004-440000-4-400004-444-40000000000000000000000000000000000000000000000
χ694-4-440000-24-4000022−2i32i32i3−2i3-2-222-2−2i32i32i3−2i3000000000000000000000000000000000000000000
χ704-4-440000-24-40000222i3−2i3−2i32i3-2-222-22i3−2i3−2i32i3000000000000000000000000000000000000000000
χ714-4-440000-2-44000022−2i32i32i3−2i3-22-2-222i3−2i3−2i32i3000000000000000000000000000000000000000000
χ724-4-440000-2-440000222i3−2i3−2i32i3-22-2-22−2i32i32i3−2i3000000000000000000000000000000000000000000

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