Finite Group Databasebeta

← Group #13168084

Character table — Group #13168084

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order12223334466666666633366666666612121212121212121212226666366612121212121212122444466666666121212121212121212122244446661212121212121212121212444661212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11111111111111111111111-1-1111-11-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-111111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-11-111-1-1111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1111-1-11111-1-1-11111-1-1-1-111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-111-1-1-11111-1-111-1-1-1-1-111
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-11-1-1-1-1111-1-111-1-1-1-111111-1-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-1-1-11-1-111-1-11111-11-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-11111-1-1-11111-1-1-1-11-11
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-111-1-1111111-1-111-1-1111-1-111-1-1-111-1-111-1-1-11111-1-1111-1-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-111-1-1111111-1-111111111-1-1-11-1-1-1-111-1-11-1-111-1-111-1-1-111
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111-11111-1-11-1-111-1-1-1-111-1-11-11
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1111-1-111-11111-1-111-1-111-11-1
χ17222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-12202022-1-1-1-1-1-1-1-1-1-122-1-1-1-12222002-1-102000-1-10000000-1-1-1-1000000000
χ18222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-20202211-1-1-1-1-1-11122-1-1-1-1-2-2-2-200-2110-20001100000001111000000000
χ19222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1220-20-2-2-1-1111111-1-1-2-21111-2-2-2-2002-1-102000-1-100000001111000000000
χ20222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1-2-20-20-2-21111111111-2-21111222200-2110-2000110000000-1-1-1-1000000000
χ21222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-2111122-1-1-1-1-1-1-1-111-2-211112-20-2022-1-1-1-1-1-11111-2-2111122-2-2002-1-10-2000110000000-1-111000000000
χ22222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-2111122-1-1-1-1-1-1-1-111-2-21111-220-202211-1-1-1-111-1-1-2-21111-2-22200-21102000-1-1000000011-1-1000000000
χ23222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-21111-1-1-1-111-2-211112-2020-2-2-1-11111-1-11122-1-1-1-1-2-222002-1-10-200011000000011-1-1000000000
χ24222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-21111-1-1-1-111-2-21111-22020-2-2111111-1-1-1-122-1-1-1-122-2-200-21102000-1-10000000-1-111000000000
χ2522222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-122202002200000022000000000022-1-1-1-1-12-12-1-1-1-1-1-10200000-1-1-1-100000
χ2622222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-122-20-20022000000220000000000-2-2-1-1-11-1-21-2-1-111110-200000111100000
χ2722222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-220200-2-2000000-2-20000000000-2-2111-112-1211-1-1-1-10-200000111100000
χ2822222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-200-2-2000000-2-200000000002211111-21-21111110200000-1-1-1-100000
χ2922222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-1111111112-220-20022000000-2-20000000000-2-2-1-1-1112-1-211-1-1110200000-1-11100000
χ3022222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-1111111112-2-2020022000000-2-2000000000022-1-1-1-11-2121111-1-10-20000011-1-100000
χ3122222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-2220-200-2-2000000220000000000221111-12-1-2-1-1-1-1110-20000011-1-100000
χ3222222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-22-20200-2-2000000220000000000-2-2111-1-1-212-1-111-1-10200000-1-11100000
χ332222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-100222-1-100-1-1-1-12200-1-1-1-1-1-100000000020-12-100-1-1-1-12020000000000-1-10
χ342222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-100-22-2-1-100-1-1-1-12200-1-1-1-1-1-1000000000-201-21001111-20-20000000000110
χ352222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1002-2211001111-2-20011111100000000020-12-100-1-1-1-1-20-20000000000110
χ362222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-100-2-2-211001111-2-200111111000000000-201-210011112020000000000-1-10
χ372222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111222222-1-1-1-1-2-2111111002-2-2-1-100-1-1-1-1-2-200111111000000000-20-12100-1-111-20200000000001-10
χ382222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111222222-1-1-1-1-2-211111100-2-22-1-100-1-1-1-1-2-200111111000000000201-2-10011-1-120-20000000000-110
χ392222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-1-2-21111110022-2110011112200-1-1-1-1-1-1000000000-20-12100-1-11120-20000000000-110
χ402222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-1-2-211111100-222110011112200-1-1-1-1-1-1000000000201-2-10011-1-1-20200000000001-10
χ4122-2-2222002-2-2-2-22-22-222222-2-2-2-22-2-200000000002-222-2-222-2-200000000000002-20022-2-2000000000000002i−2i000000000000000000000002i−2i2i−2i000
χ4222-2-2222002-2-2-2-22-22-222222-2-2-2-22-2-200000000002-222-2-222-2-200000000000002-20022-2-200000000000000−2i2i00000000000000000000000−2i2i−2i2i000
χ4322-2-2222002-2-2-2-22-22-222222-2-2-2-22-2-20000000000-22-2-22222-2-20000000000000-2200-2-222000000000000002i−2i000000000000000000000002i−2i−2i2i000
χ4422-2-2222002-2-2-2-22-22-222222-2-2-2-22-2-20000000000-22-2-22222-2-20000000000000-2200-2-22200000000000000−2i2i00000000000000000000000−2i2i2i−2i000
χ452-22-22222i−2i-22-2-22-22-2-2222-2-222-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i0000002-22-22i−2i2i−2i2i2i−2i−2i000000000000000000000002-22i−2i00000000000000000002-22i−2i000000000
χ462-22-22222i−2i-22-2-22-22-2-2222-2-222-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i0000002-22-22i−2i2i−2i2i2i−2i−2i00000000000000000000000-22−2i2i0000000000000000000-22−2i2i000000000
χ472-22-2222−2i2i-22-2-22-22-2-2222-2-222-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000002-22-2−2i2i−2i2i−2i−2i2i2i000000000000000000000002-2−2i2i00000000000000000002-2−2i2i000000000
χ482-22-2222−2i2i-22-2-22-22-2-2222-2-222-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000002-22-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000-222i−2i0000000000000000000-222i−2i000000000
χ492-22-222-12i−2i-2-1-212-221-22-1-1-21-1-1121-212i−2i−ii2i−2i−i−iii00−i3i3−i3i3-11-11−ii2i−2i−i−iii0000000−i3i3−i3i3−i3i33−33−30033−3−32-22i−2i000−i3i3000003−30000000-11−ii000000000
χ502-22-222-12i−2i-2-1-212-221-22-1-1-21-1-1121-212i−2i−ii2i−2i−i−iii00−i3i3−i3i3-11-11−ii2i−2i−i−iii0000000i3−i3−i3i3−i3i33−3−330033−3−3-22−2i2i000i3−i300000−3300000001-1i−i000000000
χ512-22-222-12i−2i-2-1-212-221-22-1-1-21-1-1121-212i−2i−ii2i−2i−i−iii00i3−i3i3−i3-11-11−ii2i−2i−i−iii0000000−i3i3i3−i3i3−i3−333−300−3−333-22−2i2i000−i3i3000003−300000001-1i−i000000000
χ522-22-222-12i−2i-2-1-212-221-22-1-1-21-1-1121-212i−2i−ii2i−2i−i−iii00i3−i3i3−i3-11-11−ii2i−2i−i−iii0000000i3−i3i3−i3i3−i3−33−3300−3−3332-22i−2i000i3−i300000−330000000-11−ii000000000
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χ814-44-44-2-24i−4i-4-22242-22-4-2-2122-21-1-2-122−2i2i−2i2i4i−4i−2i−2i2i2i0000001-11-1i−i−2i2iii−i−i0000000−2i32i300000023−230000000000000i3−i300000−3300000000000000000000
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χ874-44-4-24-24i−4i2-2-42-2-4422-21-22-11-22-222-14i−4i−2i2i−2i2iii−i−i00−2i32i3−2i32i31-11-1−2i2i−2i2iii−i−i000000000i3−i3i3−i323−230000−3−333000000000000000000000000000000000000
χ884-44-4-24-24i−4i2-2-42-2-4422-21-22-11-22-222-14i−4i−2i2i−2i2iii−i−i002i3−2i32i3−2i31-11-1−2i2i−2i2iii−i−i000000000−i3i3−i3i3−2323000033−3−3000000000000000000000000000000000000
χ894-44-4-24-2−4i4i2-2-42-2-4422-21-22-11-22-222-1−4i4i2i−2i2i−2i−i−iii00−2i32i3−2i32i31-11-12i−2i2i−2i−i−iii000000000i3−i3i3−i3−2323000033−3−3000000000000000000000000000000000000
χ904-44-4-24-2−4i4i2-2-42-2-4422-21-22-11-22-222-1−4i4i2i−2i2i−2i−i−iii002i3−2i32i3−2i31-11-12i−2i2i−2i−i−iii000000000−i3i3−i3i323−230000−3−333000000000000000000000000000000000000
χ914-44-4-2-244i−4i242-4-22-2-421-2-2-12-2-2212-12−2i2i4i−4i−2i2i−2i−2i2i2i0000001-11-1−2i2ii−iii−i−i0000000000000000000000000000000000000003-33i−3i0000000000000000
χ924-44-4-2-244i−4i242-4-22-2-421-2-2-12-2-2212-12−2i2i4i−4i−2i2i−2i−2i2i2i0000001-11-1−2i2ii−iii−i−i000000000000000000000000000000000000000-33−3i3i0000000000000000
χ934-44-4-2-24−4i4i242-4-22-2-421-2-2-12-2-2212-122i−2i−4i4i2i−2i2i2i−2i−2i0000001-11-12i−2i−ii−i−iii0000000000000000000000000000000000000003-3−3i3i0000000000000000
χ944-44-4-2-24−4i4i242-4-22-2-421-2-2-12-2-2212-122i−2i−4i4i2i−2i2i2i−2i−2i0000001-11-12i−2i−ii−i−iii000000000000000000000000000000000000000-333i−3i0000000000000000
χ954-4-4444400-4-444-4-4-4-44444-4-4-4-44-4-44400000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ964-4-4444-200-424-2-4-4-4244-2-2-4222-2-424-2000000000000−2i32i32i3−2i3-222-200000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ974-4-4444-200-424-2-4-4-4244-2-2-4222-2-424-20000000000002i3−2i3−2i32i3-222-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ984-4-444-2400-4-4-24-422-44-24-22-4-42-222-240000000000000000-222-2000000000000000000000000000000000000000000000000000000000023−230000000
χ994-4-444-2400-4-4-24-422-44-24-22-4-42-222-240000000000000000-222-20000000000000000000000000000000000000000000000000000000000−23230000000
χ1004-4-44-244002-4442-4-4-4-2-2-24222-442-4-2-20000000000000000-222-20000000000000000000000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000
χ1014-4-44-244002-4442-4-4-4-2-2-24222-442-4-2-20000000000000000-222-200000000000000000000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000
χ1024-4-44-24-200224-22-4-42-2-21-22-1-12-222-210000003-3-3300−2i32i32i3−2i31-1-1100003-3-33000000000i3−i3−i3i300002i3−2i3−i3i3i3−i3000000000000000000000000000000000000
χ1034-4-44-24-200224-22-4-42-2-21-22-1-12-222-210000003-3-33002i3−2i3−2i32i31-1-1100003-3-33000000000−i3i3i3−i30000−2i32i3i3−i3−i3i3000000000000000000000000000000000000
χ1044-4-44-24-200224-22-4-42-2-21-22-1-12-222-21000000-333-300−2i32i32i3−2i31-1-110000-333-3000000000i3−i3−i3i30000−2i32i3i3−i3−i3i3000000000000000000000000000000000000
χ1054-4-44-24-200224-22-4-42-2-21-22-1-12-222-21000000-333-3002i3−2i3−2i32i31-1-110000-333-3000000000−i3i3i3−i300002i3−2i3−i3i3i3−i3000000000000000000000000000000000000
χ1068888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-42222000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-2000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10888-8-88-4-4008444-8-44-4-8-4-42-4-44-2-24244000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4800-4-84-84-44842-4-42-4444-2-4-24000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-400-44444-44-4422222-2-2-2-22-2-20000006i−6i6i−6i000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-44444-44-4422222-2-2-2-22-2-2000000−6i6i−6i6i000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-48i−8i4-444-44-444222-2-222-22-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-11-112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4−8i8i4-444-44-444222-2-222-22-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-11-11−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000
χ1148-8-888-4-400-84-4-4-84448-4-42444-224-2-4-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48004-8-48444-8-42-4-4-2444-4-242-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044-4-44444-4222-2-2-2-22-2-2220000006-6-66000000-111-10000-333-300000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044-4-44444-4222-2-2-2-22-2-222000000-666-6000000-111-100003-3-3300000000000000000000000000000000000000000000000000000000000

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