Finite Group Databasebeta

← Group #13168065

Character table — Group #13168065

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order1222333446666666663336666666661212121212121212121222666636661212121212121212224446666666612121212121212121212224444666666612121212121212444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-111-111111111111111111111-1-1111-1-111-1-1-11-111-1-1-1-1-111-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-111-1111-1-1111111-1-1111111-1-1-1-1-1-1-111-1-1111-11-1-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111111111-1-11-1-111-1-111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11-111-1-111-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1111-11-1-111-1-1-111-1-111-1-111-1-11
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
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-111
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-1-11-11-1-111-11-11111-1-1-1-1111-1-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-111-1-1-1-1-1-1-1-11111-111-1-111-11-111-1-11-1-1-1-11111-1-111-11-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111-111-1-1-1-11111-1-11-11
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-1-111-1-1-1-111-1-1111111-1-111111-1-111-1-11-11-1-1111-1-1-1-11111-1-1-1-1-111
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1-111-11-111-1-1-11-11111-1-1-1-1-1-11-11
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-11111-11-1
χ17222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12022022-1-1-1-1-1-1-1-1-1-122-1-1-1-1220022200-1-100020-1-100000-1-100-1-10000000
χ18222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-202-202211-1-1-1-1-1-11122-1-1-1-1-2-200-2-2-20011000-2011000001100110000000
χ19222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-120-220-2-2-1-1111111-1-1-2-21111-2-200-2-2200-1-100020-1-1000001100110000000
χ20222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-1-20-2-20-2-21111111111-2-21111220022-20011000-201100000-1-100-1-10000000
χ21222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-2111122-1-1-1-1-1-1-1-1-2-211111120-2-2022-1-1-1-1-1-11111-2-211112200-2-2200-1-1000-201100000-1-100110000000
χ22222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-2111122-1-1-1-1-1-1-1-1-2-2111111-20-2202211-1-1-1-111-1-1-2-21111-2-20022-2001100020-1-1000001100-1-10000000
χ23222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111-2-21111-1-1-1-1-2-2111111202-20-2-2-1-11111-1-11122-1-1-1-1-2-20022200-1-1000-2011000001100-1-10000000
χ24222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111-2-21111-1-1-1-1-2-2111111-20220-2-2111111-1-1-1-122-1-1-1-12200-2-2-2001100020-1-100000-1-100110000000
χ2522222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-102202-1-100-1-1-1-12200-1-1-1-1-1-100000002-100-1-1-10200-1-12200000000000-1-10
χ2622222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-10-220-2-1-100-1-1-1-12200-1-1-1-1-1-10000000-21001110-20011-2-200000000000110
χ2722222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-102-20211001111-2-20011111100000002-100-1-1-10200-1-1-2-200000000000110
χ2822222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-10-2-20-211001111-2-2001111110000000-21001110-200112200000000000-1-10
χ2922222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111222222-1-1-1-111-2-2111102-20-2-1-100-1-1-1-1-2-20011111100000002-100-1-110-200112-2000000000001-10
χ3022222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111222222-1-1-1-111-2-211110-2-202-1-100-1-1-1-1-2-2001111110000000-210011-10200-1-1-2200000000000-110
χ3122222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-111-2-211110220-2110011112200-1-1-1-1-1-100000002-100-1-110-20011-2200000000000-110
χ3222222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-111-2-211110-2202110011112200-1-1-1-1-1-10000000-210011-10200-1-12-2000000000001-10
χ332222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-122022002200000022000000002200-1-12-1-1-1-12-1-1-1-1-1-100200-1-100-1-100000
χ342222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-12-202-200220000002200000000-2-200-11-2-1-111-2-11-1-11100-20011001100000
χ352222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-220-2200-2-2000000-2-200000000-2-2001-1211-1-121-111-1-100-20011001100000
χ362222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-200-2-2000000-2-200000000220011-21111-211111100200-1-100-1-100000
χ372222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111220-2-20022000000-2-200000000-2-200-1-12-1-1-1-1-2111111002001100-1-100000
χ382222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-1111111112-20-220022000000-2-2000000002200-11-2-1-11121-111-1-100-200-1-1001100000
χ392222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-2202-200-2-2000000220000000022001-1211-1-1-2-11-1-11100-200-1-1001100000
χ402222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111-2-202200-2-20000002200000000-2-20011-211112-1-1-1-1-1-1002001100-1-100000
χ4122-2-222200-22-22-2-2-22-2222-2-2-2-222-2-2200000000002-222-2-22-2-2200000000000002-20022-2-20000000000002i−2i0000000000000000000002i−2i00002i−2i000
χ4222-2-222200-22-22-2-2-22-2222-2-2-2-222-2-2200000000002-222-2-22-2-2200000000000002-20022-2-2000000000000−2i2i000000000000000000000−2i2i0000−2i2i000
χ4322-2-222200-22-22-2-2-22-2222-2-2-2-222-2-220000000000-22-2-2222-2-220000000000000-2200-2-2220000000000002i−2i0000000000000000000002i−2i0000−2i2i000
χ4422-2-222200-22-22-2-2-22-2222-2-2-2-222-2-220000000000-22-2-2222-2-220000000000000-2200-2-222000000000000−2i2i000000000000000000000−2i2i00002i−2i000
χ452-22-22222i−2i2-2-2-222-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i000000000000000000000002-2002i−2i000000000000000002-2002i−2i0000000
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χ482-22-2222−2i2i2-2-2-222-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000-22002i−2i00000000000000000-22002i−2i0000000
χ492-22-222-12i−2i-1-2-21221-2-22-1-12-1-11-21-2112i−2i−ii2i−2i−i−iii00−i3i3−i3i3-1-1112i−2i−ii−i−iii0000000−i3i3−i3i3−i3i33−33−30033−3−32-2002i−2i000−i3i3000003−300000-1100−ii0000000
χ502-22-222-12i−2i-1-2-21221-2-22-1-12-1-11-21-2112i−2i−ii2i−2i−i−iii00−i3i3−i3i3-1-1112i−2i−ii−i−iii0000000i3−i3−i3i3−i3i33−3−330033−3−3-2200−2i2i000i3−i300000−33000001-100i−i0000000
χ512-22-222-12i−2i-1-2-21221-2-22-1-12-1-11-21-2112i−2i−ii2i−2i−i−iii00i3−i3i3−i3-1-1112i−2i−ii−i−iii0000000−i3i3i3−i3i3−i3−333−300−3−333-2200−2i2i000−i3i3000003−3000001-100i−i0000000
χ522-22-222-12i−2i-1-2-21221-2-22-1-12-1-11-21-2112i−2i−ii2i−2i−i−iii00i3−i3i3−i3-1-1112i−2i−ii−i−iii0000000i3−i3i3−i3i3−i3−33−3300−3−3332-2002i−2i000i3−i300000−3300000-1100−ii0000000
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χ542-22-222-1−2i2i-1-2-21221-2-22-1-12-1-11-21-211−2i2ii−i−2i2iii−i−i00−i3i3−i3i3-1-111−2i2ii−iii−i−i0000000i3−i3−i3i3−i3i3−333−300−3−333-22002i−2i000i3−i3000003−3000001-100−ii0000000
χ552-22-222-1−2i2i-1-2-21221-2-22-1-12-1-11-21-211−2i2ii−i−2i2iii−i−i00i3−i3i3−i3-1-111−2i2ii−iii−i−i0000000−i3i3i3−i3i3−i33−3−330033−3−3-22002i−2i000−i3i300000−33000001-100−ii0000000
χ562-22-222-1−2i2i-1-2-21221-2-22-1-12-1-11-21-211−2i2ii−i−2i2iii−i−i00i3−i3i3−i3-1-111−2i2ii−iii−i−i0000000i3−i3i3−i3i3−i33−33−30033−3−32-200−2i2i000i3−i3000003−300000-1100i−i0000000
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χ814-44-44-2-24i−4i-2-4224-222-4-2-21-2-21-12222-14i−4i−2i2i−2i2iii−i−i00−2i32i3−2i32i311-1-1−2i2i−2i2iii−i−i000000000i3−i3i3−i323−230000−3−333000000000000000000000000000000000000
χ824-44-44-2-24i−4i-2-4224-222-4-2-21-2-21-12222-14i−4i−2i2i−2i2iii−i−i002i3−2i32i3−2i311-1-1−2i2i−2i2iii−i−i000000000−i3i3−i3i3−2323000033−3−3000000000000000000000000000000000000
χ834-44-44-2-2−4i4i-2-4224-222-4-2-21-2-21-12222-1−4i4i2i−2i2i−2i−i−iii00−2i32i3−2i32i311-1-12i−2i2i−2i−i−iii000000000i3−i3i3−i3−2323000033−3−3000000000000000000000000000000000000
χ844-44-44-2-2−4i4i-2-4224-222-4-2-21-2-21-12222-1−4i4i2i−2i2i−2i−i−iii002i3−2i32i3−2i311-1-12i−2i2i−2i−i−iii000000000−i3i3−i3i323−230000−3−333000000000000000000000000000000000000
χ854-44-4-2444i−4i42-4-4-24-4-42-2-24-2-24-42222-4−2i2i4i−4i4i−4i4i4i−4i−4i000000-2-222−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000
χ864-44-4-244−4i4i42-4-4-24-4-42-2-24-2-24-42222-42i−2i−4i4i−4i4i−4i−4i4i4i000000-2-2222i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000000
χ874-44-4-24-24i−4i-22-42-242-42-21-2-21-222-12-12−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i0000000−2i32i300000023−23000000000000000i3−i300000−33000000000000000000
χ884-44-4-24-24i−4i-22-42-242-42-21-2-21-222-12-12−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i00000002i3−2i3000000−2323000000000000000−i3i3000003−3000000000000000000
χ894-44-4-24-2−4i4i-22-42-242-42-21-2-21-222-12-122i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii0000000−2i32i3000000−2323000000000000000i3−i3000003−3000000000000000000
χ904-44-4-24-2−4i4i-22-42-242-42-21-2-21-222-12-122i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii00000002i3−2i300000023−23000000000000000−i3i300000−33000000000000000000
χ914-44-4-2-244i−4i422-4-2-2-4221-2-21-2-22-12-122−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i00000000000000000000000000000000003-3000003i−3i0000000000000000
χ924-44-4-2-244i−4i422-4-2-2-4221-2-21-2-22-12-122−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i0000000000000000000000000000000000-3300000−3i3i0000000000000000
χ934-44-4-2-24−4i4i422-4-2-2-4221-2-21-2-22-12-1222i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii00000000000000000000000000000000003-300000−3i3i0000000000000000
χ944-44-4-2-24−4i4i422-4-2-2-4221-2-21-2-22-12-1222i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii0000000000000000000000000000000000-33000003i−3i0000000000000000
χ954-4-4444400-4-44-4-4-44-44444-4-4-44-4-444-400000000000000004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ964-4-4444-2002-442-4-4-2-444-2-2-422-2-424-22000000000000−2i32i32i3−2i3-22-2200000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ974-4-4444-2002-442-4-4-2-444-2-2-422-2-424-220000000000002i3−2i3−2i32i3-22-22000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ984-4-444-2400-4-4-2-4-42424-24-22-42-22-4-2420000000000000000-22-22000000000000000000000000023−2323−23−2323000000000000000000000000000000000000
χ994-4-444-2400-4-4-2-4-42424-24-22-42-22-4-2420000000000000000-22-220000000000000000000000000−2323−232323−23000000000000000000000000000000000000
χ1004-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-10000003i−3i−3i3i00−2i32i32i3−2i31-11-100003i−3i−3i3i000000000i3−i3−i3i30000−23233−3−33000000000000000000000000000000000000
χ1014-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-10000003i−3i−3i3i002i3−2i3−2i32i31-11-100003i−3i−3i3i000000000−i3i3i3−i3000023−23−333−3000000000000000000000000000000000000
χ1024-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-1000000−3i3i3i−3i00−2i32i32i3−2i31-11-10000−3i3i3i−3i000000000i3−i3−i3i3000023−23−333−3000000000000000000000000000000000000
χ1034-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-1000000−3i3i3i−3i002i3−2i3−2i32i31-11-10000−3i3i3i−3i000000000−i3i3i3−i30000−23233−3−33000000000000000000000000000000000000
χ1044-4-44-24400-424-42-44-4-2-2-2422-4422-2-2-40000000000000000-22-22000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ1054-4-44-24400-424-42-44-4-2-2-2422-4422-2-2-40000000000000000-22-220000000000000000000000000000000000000000000000000000000000002i3−2i300000
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
χ10888-8-8-48-4004-4-8-44-8484-42-44-244-424-2-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4800-8-44844-8-442-4-4-24442-4-24-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4004-44-4444-44222-2-2-2-222-2-220000006-66-6000000-111-10000-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-4004-44-4444-44222-2-2-2-222-2-22000000-66-66000000-111-100003-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-48i−8i-4444-4-4444222222-2-2-2-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-1-1112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4−8i8i-4444-4-4444222222-2-2-2-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-1-111−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-40044844-8-4-8-4-42-44-24-44-2-42400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-4800-84-4-84484-42-4-4-244-4-242-4400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044-4444-44-4222-2-2-22-2-222-20000006i−6i−6i6i000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044-4444-44-4222-2-2-22-2-222-2000000−6i6i6i−6i000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000

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