Finite Group Databasebeta

← Group #13168320

Character table — Group #13168320

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212124441212121212121212121212121212121212121212121222441212121212121212121212122444661212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-1-1-11111111111111111111111-1-1-1-1-1111-1-111-1-1-11-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111111111111111111-1111-1-111-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1111-11-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111
χ51111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-1-11-1
χ61111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111-11-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-11-1-1-1-1-1-1-11111-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-1-111-11-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1-11111-1-11111-1-1-1-11111-11-1-1-1-11111-1-1-1-11-111-1-111-1-1-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-11111-1-1-1-111-1-11-11-1-1-1-1-111111-1-1111-1-1-1-1111-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1111-1-111-1-111-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1111-11111-1-1-1-11111-1-1-1-11111-1-11-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-11-1-1-1-11111-1-111-1-1-1-11111111-1-1-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11-11-1-1-1-1-11111-1111-1-111-1-1-1-1-1111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-11-111111-1-1-1-11-1-1111-1-1-1-1-1-11-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111-11111-1-1-1-111-1-11-111-1-11111-11-1-1
χ17222222-122-12-122-122-1-122-1-12-1-1-12-122-1-1-1-1-1-12222002222-1-1-1-1222-1-1-1-1-1-12022200-1-1000022-1-1-1-1-1-1-1-1-1-10000-1-12000-1-100-1-1202000000000-1-100
χ18222222-122-12-122-122-1-122-1-12-1-1-12-122-1-1-1-1-1-12222002222-1-1-1-1222-1-1-1-1-1-1-20-2-2-200-1-1000022-1-1-1-1-1-1-1-1-1-1000011-2000110011-20-20000000001100
χ19222222-122-12-122-122-1-122-1-12-1-1-12-122-1-1-1-1-1-1-2-2-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-12022200110000-2-211111111110000-1-12000-1-100-1-1-20-20000000001100
χ20222222-122-12-122-122-1-122-1-12-1-1-12-122-1-1-1-1-1-1-2-2-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-2-200110000-2-21111111111000011-2000110011202000000000-1-100
χ21222222-122-12-122-122-1-1-22-1-12-1-1-12-1-2-211111122-2-200-2-2-2-2-1-1-1-1-2-2-211111120-22200-1-100002211-1-1-1-1111100001-1-2000-1-10011-2020000000001-100
χ22222222-122-12-122-122-1-1-22-1-12-1-1-12-1-2-211111122-2-200-2-2-2-2-1-1-1-1-2-2-2111111-202-2-200-1-100002211-1-1-1-111110000-1120001100-1-120-2000000000-1100
χ23222222-122-12-122-122-1-1-22-1-12-1-1-12-1-2-2111111-2-222002222-1-1-1-1-2-2-211111120-22200110000-2-2-1-11111-1-1-1-100001-1-2000-1-1001120-2000000000-1100
χ24222222-122-12-122-122-1-1-22-1-12-1-1-12-1-2-2111111-2-222002222-1-1-1-1-2-2-2111111-202-2-200110000-2-2-1-11111-1-1-1-10000-1120001100-1-1-2020000000001-100
χ2522222-122-12-122-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-102000-1-122-1-122-1-122-1-1-1-1-1-1-1-122000002-1-100-1-1000200-1-1-1-100000000
χ2622222-122-12-122-122-12-12-12-1-12-1-1-12-1-122-1-1-1-12222-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-10-2000112211-2-2-1-122-1-1-1-1-1-1-1-1-2-200000-2110011000-200111100000000
χ2722222-122-12-122-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1-2-2-2-2221111-1-1-1-12-1-122-1-1-1-102000-1-1-2-2-1-12211-2-211111111-2-2000002-1-100-1-1000-200111100000000
χ2822222-122-12-122-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-10-200011-2-211-2-211-2-2111111112200000-2110011000200-1-1-1-100000000
χ2922222-122-12-122-122-12-1-2-12-1-12-1-1-1211-2-2111122-2-2221111-1-1-1-1-211-2-211110-2000-1-1221122-1-1-2-2-1-1-1-111112200000-21100-1-1000-200-1-11100000000
χ3022222-122-12-122-122-12-1-2-12-1-12-1-1-1211-2-2111122-2-2-2-21111-1-1-1-1-211-2-21111020001122-1-1-2-2-1-1-2-2-1-1-1-11111-2-2000002-1-1001100020011-1-100000000
χ3122222-122-12-122-122-12-1-2-12-1-12-1-1-1211-2-21111-2-22222-1-1-1-1-1-1-1-1-211-2-211110-2000-1-1-2-2112211221111-1-1-1-1-2-200000-21100-1-100020011-1-100000000
χ3222222-122-12-122-122-12-1-2-12-1-12-1-1-1211-2-21111-2-222-2-2-1-1-1-1-1-1-1-1-211-2-211110200011-2-2-1-1-2-211221111-1-1-1-122000002-1-10011000-200-1-11100000000
χ332222-122-12222-122-1-1-122-1-12-1-122-1-1222222220000220000-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1220022-1-1000000000000002222-1-1-1-1-1-1-1-1-1-100020000-1-10000-10
χ342222-122-12222-122-1-1-122-1-12-1-122-1-1222222220000220000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-211220022-1-100000000000000-2-2-2-21-1-1-111-1-111000-2000011000010
χ352222-122-12222-122-1-1-122-1-12-1-122-1-1222222220000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-12-22-1-1-2-200-2-21100000000000000-2-222-1111-1-111-1-1000-2000011000010
χ362222-122-12222-122-1-1-122-1-12-1-122-1-1222222220000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211-2-200-2-2110000000000000022-2-2111111111100020000-1-10000-10
χ372222-122-12222-122-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20000220000-1-1-1-11111111112-2-2-1-12200-2-2-1-10000000000000022-221111-1-1-1-111000-20000-1-1000010
χ382222-122-12222-122-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20000220000-1-1-1-1111111111-2-22112200-2-2-1-100000000000000-2-22-2-111111-1-1-1-100020000110000-10
χ392222-122-12222-122-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20000-2-20000-1-1-1-111111111122-2-1-1-2-200221100000000000000-2-2-221-1-1-1-1-1111100020000110000-10
χ402222-122-12222-122-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20000-2-20000-1-1-1-1111111111-22211-2-200221100000000000000222-2-1-1-1-11111-1-1000-20000-1-1000010
χ412-22-2222-2-2-22-2-2-2222220-22-22-22-2-2-2000000002i−2i002i−2i000022-2-2000000000000002i−2i2i−2i002i−2i2i−2i002i2i−2i−2i00002-200000000002i−2i0000002-20000000000
χ422-22-2222-2-2-22-2-2-2222220-22-22-22-2-2-2000000002i−2i00−2i2i000022-2-200000000000000−2i2i2i−2i00−2i2i2i−2i002i2i−2i−2i0000-220000000000−2i2i000000-220000000000
χ432-22-2222-2-2-22-2-2-2222220-22-22-22-2-2-200000000−2i2i002i−2i000022-2-2000000000000002i−2i−2i2i002i−2i−2i2i00−2i−2i2i2i0000-2200000000002i−2i000000-220000000000
χ442-22-2222-2-2-22-2-2-2222220-22-22-22-2-2-200000000−2i2i00−2i2i000022-2-200000000000000−2i2i−2i2i00−2i2i−2i2i00−2i−2i2i2i00002-20000000000−2i2i0000002-20000000000
χ452-22-22-12-21-2-1-2-2122-12-10121-1-2-111-23−30033−3−32i−2i002i−2i−i3−i3i3i3-1-11103−30033−3−300000−ii2i−2i−i3i32i−2i−ii00−i−iii−i3−i3i3i32-2000000−i3i300−ii000000-113−300000000
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χ472-22-22-12-21-2-1-2-2122-12-10121-1-2-111-23−30033−3−3−2i2i002i−2ii3i3−i3−i3-1-11103−30033−3−300000−ii−2i2i−i3i32i−2ii−i00ii−i−ii3i3−i3−i3-22000000−i3i300−ii0000001-1−3300000000
χ482-22-22-12-21-2-1-2-2122-12-10121-1-2-111-23−30033−3−3−2i2i00−2i2ii3i3−i3−i3-1-11103−30033−3−300000i−i−2i2ii3−i3−2i2ii−i00ii−i−ii3i3−i3−i32-2000000i3−i300i−i000000-113−300000000
χ492-22-22-12-21-2-1-2-2122-12-10121-1-2-111-2−3300−3−3332i−2i002i−2ii3i3−i3−i3-1-1110−3300−3−33300000−ii2i−2ii3−i32i−2i−ii00−i−iiii3i3−i3−i32-2000000i3−i300−ii000000-11−3300000000
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χ8344-4-4-24-2-2-42-4-22422-21-20-2-12212-22-100−2323−2323−232300000000001-11-10003−33−33−30002i3−2i3000000000000000000000000000000−i3i3003i−3i0000000000000000
χ844-44-444-2-4-4242-4-4-244-2-20-4-2242-22-42000000004i−4i00000000-2-2220000000000000000−2i2i00004i−4i00−2i−2i2i2i000000000000000000000000000000000000
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χ864-44-44-2-2-422-22-42-24-2-2102-2-1-221-12223−2300−3−3334i−4i0000−2i3−2i32i32i311-1-1023−2300−3−3330000000−2i2i0000−2i2i00ii−i−ii3i3−i3−i300000000000000000000000000000000
χ874-44-44-2-2-422-22-42-24-2-2102-2-1-221-12223−2300−3−333−4i4i00002i32i3−2i3−2i311-1-1023−2300−3−33300000002i−2i00002i−2i00−i−iii−i3−i3i3i300000000000000000000000000000000
χ884-44-44-2-2-422-22-42-24-2-2102-2-1-221-122−23230033−3−34i−4i00002i32i3−2i3−2i311-1-10−23230033−3−30000000−2i2i0000−2i2i00ii−i−i−i3−i3i3i300000000000000000000000000000000
χ894-44-44-2-2-422-22-42-24-2-2102-2-1-221-122−23230033−3−3−4i4i0000−2i3−2i32i32i311-1-10−23230033−3−300000002i−2i00002i−2i00−i−iiii3i3−i3−i300000000000000000000000000000000
χ904-44-4-2442-4-44-42-44-2-2-2402-2-4-224-4220000000000004i−4i0000-2-222000000000000004i−4i0000−2i2i000000000000000000000000−2i2i000000000000000000
χ914-44-4-2442-4-44-42-44-2-2-2402-2-4-224-422000000000000−4i4i0000-2-22200000000000000−4i4i00002i−2i0000000000000000000000002i−2i000000000000000000
χ924-44-4-2-2422-4-2-4224-21-2-20-1-2212-22-1223−23002323−23−2300004i−4i000011-1-10−3300−3−33300000−2i2i00−2i32i3−2i2i00000000000000000000i3−i300i−i000000000000000000
χ934-44-4-2-2422-4-2-4224-21-2-20-1-2212-22-1223−23002323−23−230000−4i4i000011-1-10−3300−3−333000002i−2i002i3−2i32i−2i00000000000000000000−i3i300−ii000000000000000000
χ944-44-4-2-2422-4-2-4224-21-2-20-1-2212-22-12−232300−23−23232300004i−4i000011-1-103−30033−3−300000−2i2i002i3−2i3−2i2i00000000000000000000−i3i300i−i000000000000000000
χ954-44-4-2-2422-4-2-4224-21-2-20-1-2212-22-12−232300−23−2323230000−4i4i000011-1-103−30033−3−3000002i−2i00−2i32i32i−2i00000000000000000000i3−i300−ii000000000000000000
χ964-4-4444-2-44-2-424-42-44-2-20-42-2-42224-200000000004i−4i004i−4i4i−4i-222-2000000000000000000000000−2i2i0000−2i2i−2i2i00000000000000000000000000000000
χ974-4-4444-2-44-2-424-42-44-2-20-42-2-42224-20000000000−4i4i00−4i4i−4i4i-222-20000000000000000000000002i−2i00002i−2i2i−2i00000000000000000000000000000000
χ984-4-444-24-4-242-442-4-4-24-202-4-22-422-2400000000004i−4i00−2i2i−2i2i-222-20000000000000000000000004i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ994-4-444-24-4-242-442-4-4-24-202-4-22-422-240000000000−4i4i002i−2i2i−2i-222-2000000000000000000000000−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ1004-4-444-2-2-4-2-222422-4-2-21022122-1-1-2-200003-3-33004i−4i00−2i2i−2i2i1-1-11000003-3-33000000000000000−2i2i3i−3i−3i3ii−ii−i00000000000000000000000000000000
χ1014-4-444-2-2-4-2-222422-4-2-21022122-1-1-2-200003-3-3300−4i4i002i−2i2i−2i1-1-11000003-3-330000000000000002i−2i−3i3i3i−3i−ii−ii00000000000000000000000000000000
χ1024-4-444-2-2-4-2-222422-4-2-21022122-1-1-2-20000-333-3004i−4i00−2i2i−2i2i1-1-1100000-333-3000000000000000−2i2i−3i3i3i−3ii−ii−i00000000000000000000000000000000
χ1034-4-444-2-2-4-2-222422-4-2-21022122-1-1-2-20000-333-300−4i4i002i−2i2i−2i1-1-1100000-333-30000000000000002i−2i3i−3i−3i3i−ii−ii00000000000000000000000000000000
χ1044-4-44-244244-4-4-2-4-42-2-24022422-4-4-2-2000000000000000000-222-20000000000000000000000000000000000004i−4i00000000000000000000−2i2i000000
χ1054-4-44-244244-4-4-2-4-42-2-24022422-4-4-2-2000000000000000000-222-2000000000000000000000000000000000000−4i4i000000000000000000002i−2i000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-48-44-8484-4-842-4-40244-2-44-4-240000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-4-4444-44-44422202-2-2-22-22-2-20043−43−2323−23230000000000-11-11000−23233−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4-4444-44-44422202-2-2-22-22-2-200−434323−2323−230000000000-11-1100023−23−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-8-48-44-84844-8-4-4-42-40424-4-2-444-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-4444-4444-4-42220-22-22-22-2-2-243−4300−23−2323230000000000-1-1110−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4444-4444-4-42220-22-22-22-2-2-2−4343002323−23−230000000000-1-111023−2300−3−333000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-448-4-84-4-844-42-404-2-44-244-420000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-484-484-8-44-842-4-40-24-4-24442-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-44-4-444-44442220-2-22-2-2-2-22200006-6-660000000000-111-100000-333-3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-44-4-444-44442220-2-22-2-2-2-2220000-666-60000000000-111-1000003-3-33000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).