Finite Group Databasebeta

← Group #67666

Character table — Group #67666

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order1222223444444446661212121212121212121212124466888888881212121212122424242424242424242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i
χ6111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii
χ7111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii
χ8111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i
χ91111-1-11111111-1-1111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ101111-1-11111111-1-1111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ111111-1-11111111-1-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii
χ121111-1-11111111-1-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i
χ131111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1
χ141111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11
χ151111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11
χ161111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1
χ172222222-2-222-2-222222-2-2-2-22222-2-2-2-2-2-22200000000-2-222-2-2000000000000000000000000
χ182222222-2-2-2-222-2-2222-2-2-2-2-2-2-2-22222-222200000000-2-2-2-222000000000000000000000000
χ19222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ20222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111111100000000
χ21222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-12i2i2i2i−2i−2i−2i−2i-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000
χ22222222-122-2-2-2-2-2-2-1-1-1-1-1-1-1111111112-2-1-1−2i−2i−2i−2i2i2i2i2i-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000
χ23222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-11133−3−333−3−333−3−333−3−300000000
χ24222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-2-1-10000000011-1-111−3−333−3−333−3−333−3−33300000000
χ25222222-1-2-2-2-222-2-2-1-1-111111111-1-1-1-1-22-1-1000000001111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000
χ26222222-1-2-2-2-222-2-2-1-1-111111111-1-1-1-1-22-1-1000000001111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000
χ272222-2-22-2-222-2-2-2-2222-2-2-2-22222-2-2-2-222-2-20000000022-2-222000000000000000000000000
χ282222-2-22-2-2-2-22222222-2-2-2-2-2-2-2-222222-2-2-2000000002222-2-2000000000000000000000000
χ292222-2-2-1222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-222-2-2111111-1-1-1-11111-1-1-1-1111100000000
χ302222-2-2-1222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-2-2221111111111-1-1-1-11111-1-1-1-100000000
χ312222-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000
χ322222-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000
χ332222-2-2-1-2-222-2-2-2-2-1-1-11111-1-1-1-11111221100000000-1-111-1-133−3−3−3−33333−3−3−3−33300000000
χ342222-2-2-1-2-222-2-2-2-2-1-1-11111-1-1-1-11111221100000000-1-111-1-1−3−33333−3−3−3−33333−3−300000000
χ352222-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000
χ362222-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-21100000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000
χ3722-2-22-22002i−2i002i−2i2-2-200002i2i−2i−2i0000002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−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
χ3822-2-22-22002i−2i002i−2i2-2-200002i2i−2i−2i0000002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−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
χ3922-2-22-2200−2i2i00−2i2i2-2-20000−2i−2i2i2i0000002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000
χ4022-2-22-2200−2i2i00−2i2i2-2-20000−2i−2i2i2i0000002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i00−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000
χ4122-2-22-2-1002i−2i002i−2i-11133−3−3−i−iii−i3−i3i3i300-111+i−1−i1+i−1−i1−i−1+i1−i−1+i3−3−ii−i3i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ4222-2-22-2-1002i−2i002i−2i-11133−3−3−i−iii−i3−i3i3i300-11−1−i1+i−1−i1+i−1+i1−i−1+i1−i3−3−ii−i3i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ4322-2-22-2-1002i−2i002i−2i-111−3−333−i−iiii3i3−i3−i300-111+i−1−i1+i−1−i1−i−1+i1−i−1+i−33−iii3−i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ4422-2-22-2-1002i−2i002i−2i-111−3−333−i−iiii3i3−i3−i300-11−1−i1+i−1−i1+i−1+i1−i−1+i1−i−33−iii3−i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ4522-2-22-2-100−2i2i00−2i2i-11133−3−3ii−i−ii3i3−i3−i300-111−i−1+i1−i−1+i1+i−1−i1+i−1−i3−3i−ii3−i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ4622-2-22-2-100−2i2i00−2i2i-11133−3−3ii−i−ii3i3−i3−i300-11−1+i1−i−1+i1−i−1−i1+i−1−i1+i3−3i−ii3−i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ4722-2-22-2-100−2i2i00−2i2i-111−3−333ii−i−i−i3−i3i3i300-111−i−1+i1−i−1+i1+i−1−i1+i−1−i−33i−i−i3i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ4822-2-22-2-100−2i2i00−2i2i-111−3−333ii−i−i−i3−i3i3i300-11−1+i1−i−1+i1−i−1−i1+i−1−i1+i−33i−i−i3i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ4922-2-2-222002i−2i00−2i2i2-2-200002i2i−2i−2i000000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i00−2i2i001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ5022-2-2-222002i−2i00−2i2i2-2-200002i2i−2i−2i000000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i00−2i2i00−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ5122-2-2-22200−2i2i002i−2i2-2-20000−2i−2i2i2i000000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000
χ5222-2-2-22200−2i2i002i−2i2-2-20000−2i−2i2i2i000000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i00−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00000000
χ5322-2-2-22-1002i−2i00−2i2i-11133−3−3−i−iii−i3−i3i3i3001-11+i−1−i−1−i1+i1−i−1+i−1+i1−i−33i−ii3−i3−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ5422-2-2-22-1002i−2i00−2i2i-11133−3−3−i−iii−i3−i3i3i3001-1−1−i1+i1+i−1−i−1+i1−i1−i−1+i−33i−ii3−i3ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ5522-2-2-22-1002i−2i00−2i2i-111−3−333−i−iiii3i3−i3−i3001-11+i−1−i−1−i1+i1−i−1+i−1+i1−i3−3i−i−i3i3−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ5622-2-2-22-1002i−2i00−2i2i-111−3−333−i−iiii3i3−i3−i3001-1−1−i1+i1+i−1−i−1+i1−i1−i−1+i3−3i−i−i3i3ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ5722-2-2-22-100−2i2i002i−2i-11133−3−3ii−i−ii3i3−i3−i3001-11−i−1+i−1+i1−i1+i−1−i−1−i1+i−33−ii−i3i3−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ5822-2-2-22-100−2i2i002i−2i-11133−3−3ii−i−ii3i3−i3−i3001-1−1+i1−i1−i−1+i−1−i1+i1+i−1−i−33−ii−i3i3ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ5922-2-2-22-100−2i2i002i−2i-111−3−333ii−i−i−i3−i3i3i3001-11−i−1+i−1+i1−i1+i−1−i−1−i1+i3−3−iii3−i3−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ6022-2-2-22-100−2i2i002i−2i-111−3−333ii−i−i−i3−i3i3i3001-1−1+i1−i1−i−1+i−1−i1+i1+i−1−i3−3−iii3−i3ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ614-44-400400004i−4i00-44-4000000004i−4i4i−4i000000000000000000000000000000000000000000
χ624-44-40040000−4i4i00-44-400000000−4i4i−4i4i000000000000000000000000000000000000000000
χ634-44-400-200004i−4i002-22−2i32i3−2i32i323−2323−23−2i2i−2i2i000000000000000000000000000000000000000000
χ644-44-400-200004i−4i002-222i3−2i32i3−2i3−2323−2323−2i2i−2i2i000000000000000000000000000000000000000000
χ654-44-400-20000−4i4i002-22−2i32i3−2i32i3−2323−23232i−2i2i−2i000000000000000000000000000000000000000000
χ664-44-400-20000−4i4i002-222i3−2i32i3−2i323−2323−232i−2i2i−2i000000000000000000000000000000000000000000
χ674-4-440044i−4i000000-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-44004−4i4i000000-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4400-24i−4i00000022-2−2i2i2i−2i−2i32i32i3−2i3−232323−23000000000000000000000000000000000000000000
χ704-4-4400-24i−4i00000022-2−2i2i2i−2i2i3−2i3−2i32i323−23−2323000000000000000000000000000000000000000000
χ714-4-4400-2−4i4i00000022-22i−2i−2i2i−2i32i32i3−2i323−23−2323000000000000000000000000000000000000000000
χ724-4-4400-2−4i4i00000022-22i−2i−2i2i2i3−2i3−2i32i3−232323−23000000000000000000000000000000000000000000

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