Finite Group Databasebeta

← Group #13168315

Character table — Group #13168315

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order1222333446666666663336666666661212121212121212121244121212123666121212121212121244444121212121212121212121212121212121212224444121212121212121212121212121224466121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-111111111111111111111111-1-1-1-11-11-111-1-111-1-1-1-1-111-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-11-111-1-111-1-1111111111111-1-1-1-1-1-111-11-11-1-111-1-1111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-111-1-111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11-11-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11-1-111-1-111-1-1-111-1-111-1-111-1-11
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
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-1-1-1-1-111111-1-1-1-11111-1-1111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-11-1-11111-1-1-111-1-1-1-11111-1-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-1-111-111-1-1-1-11111-111-1-1-1-111-1-11-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-11-1-1111111-1-1-1-1-1-111111-1-1-1-111-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1111-111-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-11-1-11111-1-111-111-1-1-1-111111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-11111-1-111-1-11-1-111-111-1-1-1-111-111-1-1-1-1111111-11-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-11111-11-1-1111111-1-1-1-11-1-1-1-11111-1-1-1-11-11
χ17222222-1222-12-1222-122-1-12-1-12-1-1-12-122-1-122-1-1-1-1222222-1-1-1-122-1-1-1-1-1-10202200-1-10022-1-1-1-1-1-1-1-1-1-1000000-1-1020200-1-100-1-12020000000000-1-10
χ18222222-1222-12-1222-122-1-12-1-12-1-1-12-122-1-122-1-1-1-1222222-1-1-1-122-1-1-1-1-1-10-20-2200-1-10022-1-1-1-1-1-1-1-1-1-1000000110-20-200110011-20-20000000000110
χ19222222-1222-12-1222-122-1-12-1-12-1-1-12-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-10202-2001100-2-21111111111000000-1-1020200-1-100-1-1-20-20000000000110
χ20222222-1222-12-1222-122-1-12-1-12-1-1-12-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-10-20-2-2001100-2-21111111111000000110-20-2001100112020000000000-1-10
χ21222222-1-2-22-12-1222-122-1-12-1-12-1-1-12-1-2-211-2-21111222222-1-1-1-1-2-2111111020-2-200-1-100-2-211-1-1-1-11111000000-11020-2001100-1-120-20000000000-110
χ22222222-1-2-22-12-1222-122-1-12-1-12-1-1-12-1-2-211-2-21111222222-1-1-1-1-2-21111110-202-200-1-100-2-211-1-1-1-111110000001-10-20200-1-10011-20200000000001-10
χ23222222-1-2-22-12-1222-122-1-12-1-12-1-1-12-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-1-2-2111111020-2200110022-1-11111-1-1-1-1000000-11020-2001100-1-1-20200000000001-10
χ24222222-1-2-22-12-1222-122-1-12-1-12-1-1-12-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-1-2-21111110-202200110022-1-11111-1-1-1-10000001-10-20200-1-1001120-20000000000-110
χ2522222-1222-12-1222-122-12-1-12-1-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-120202-1-122-1-1-1-122-1-1-1-1-1-1-1-1222200002020-1-100-1-100000-1-100-1-10000000
χ2622222-1222-12-1222-122-12-1-12-1-12-1-1-12-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-20-202112211-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-20-20110011000001100110000000
χ2722222-1222-12-1222-122-12-1-12-1-12-1-1-12-1-12222-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-12020-2-1-1-2-2-1-111-2-211111111-2-2-2-200002020-1-100-1-1000001100110000000
χ2822222-1222-12-1222-122-12-1-12-1-12-1-1-12-1-12222-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1-20-20-211-2-21111-2-21111111122220000-20-2011001100000-1-100-1-10000000
χ2922222-12-2-2-12-1222-122-12-1-12-1-12-1-1-1211-2-2-2-2111122-1-1-1-1-1-1-1-111-2-2111120-20-2-1-1221111-2-2-1-1-1-11111-2-222000020-201100-1-1000001100-1-10000000
χ3022222-12-2-2-12-1222-122-12-1-12-1-12-1-1-1211-2-2-2-2111122-1-1-1-1-1-1-1-111-2-21111-2020-21122-1-111-2-2-1-1-1-1111122-2-20000-2020-1-1001100000-1-100110000000
χ3122222-12-2-2-12-1222-122-12-1-12-1-12-1-1-1211-2-2-2-21111-2-21111-1-1-1-111-2-2111120-202-1-1-2-211-1-1221111-1-1-1-122-2-2000020-201100-1-100000-1-100110000000
χ3222222-12-2-2-12-1222-122-12-1-12-1-12-1-1-1211-2-2-2-21111-2-21111-1-1-1-111-2-21111-2020211-2-2-1-1-1-1221111-1-1-1-1-2-2220000-2020-1-10011000001100-1-10000000
χ332222-122222222-1-122-1-1-12-1-12-1-122-1-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-12222022002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-102000-1-100-1-100000
χ342222-122222222-1-122-1-1-12-1-12-1-122-1-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-12-22-202200220000000000000000-2-2-2-2-11-11-1-111-1-1110-200011001100000
χ352222-122222222-1-122-1-1-12-1-12-1-122-1-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-1-22-220-2-200-2-20000000000000000-2-2221-11-111-1-111-1-10-200011001100000
χ362222-122222222-1-122-1-1-12-1-12-1-122-1-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200-2-2000000000000000022-2-211111111111102000-1-100-1-100000
χ372222-122-2-22222-1-122-1-1-12-1-12-1-122-1-1-2-2-2-211-2-2-2-2000000-1-1-1-11111111122-2-202200-2-20000000000000000222-2-1-1111111-1-1-1-10-2000-1-1001100000
χ382222-122-2-22222-1-122-1-1-12-1-12-1-122-1-1-2-2-2-211-2-2-2-2000000-1-1-1-1111111112-2-2202200-2-20000000000000000-2-2-22-111-111-1-1-1-111020001100-1-100000
χ392222-122-2-22222-1-122-1-1-12-1-12-1-122-1-1-2-2-2-211-2-2-2-2000000-1-1-1-111111111-222-20-2-200220000000000000000-2-22-21-1-11-1-11111-1-1020001100-1-100000
χ402222-122-2-22222-1-122-1-1-12-1-12-1-122-1-1-2-2-2-211-2-2-2-2000000-1-1-1-111111111-2-2220-2-20022000000000000000022-2211-1-1-1-1-1-111110-2000-1-1001100000
χ412-22-22222i−2i-2-222-2-2-2-22222-2-2-2222-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i000000000000000000000002-22i−2i00000000000000000002-2002i−2i0000000
χ422-22-22222i−2i-2-222-2-2-2-22222-2-2-2222-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i00000000000000000000000-22−2i2i0000000000000000000-2200−2i2i0000000
χ432-22-2222−2i2i-2-222-2-2-2-22222-2-2-2222-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i000000000000000000000002-2−2i2i00000000000000000002-200−2i2i0000000
χ442-22-2222−2i2i-2-222-2-2-2-22222-2-2-2222-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000-222i−2i0000000000000000000-22002i−2i0000000
χ452-22-22-122i−2i1-2-12-2-21-22-12-11-21-12-111-2−ii2i−2i2i−2i−i−iii00−i3−i3i3i3-1-111−ii2i−2i−i−iii000003−300−i3i33−300−i3−i3i3i333−3−32-22i−2i00000000−i3i3003−300000-1100−ii0000000
χ462-22-22-122i−2i1-2-12-2-21-22-12-11-21-12-111-2−ii2i−2i2i−2i−i−iii00−i3−i3i3i3-1-111−ii2i−2i−i−iii00000−3300i3−i33−300−i3−i3i3i333−3−3-22−2i2i00000000i3−i300−33000001-100i−i0000000
χ472-22-22-122i−2i1-2-12-2-21-22-12-11-21-12-111-2−ii2i−2i2i−2i−i−iii00i3i3−i3−i3-1-111−ii2i−2i−i−iii000003−300−i3i3−3300i3i3−i3−i3−3−333-22−2i2i00000000−i3i3003−3000001-100i−i0000000
χ482-22-22-122i−2i1-2-12-2-21-22-12-11-21-12-111-2−ii2i−2i2i−2i−i−iii00i3i3−i3−i3-1-111−ii2i−2i−i−iii00000−3300i3−i3−3300i3i3−i3−i3−3−3332-22i−2i00000000i3−i300−3300000-1100−ii0000000
χ492-22-22-12−2i2i1-2-12-2-21-22-12-11-21-12-111-2i−i−2i2i−2i2iii−i−i00−i3−i3i3i3-1-111i−i−2i2iii−i−i000003−300i3−i3−3300−i3−i3i3i3−3−333-222i−2i00000000i3−i3003−3000001-100−ii0000000
χ502-22-22-12−2i2i1-2-12-2-21-22-12-11-21-12-111-2i−i−2i2i−2i2iii−i−i00−i3−i3i3i3-1-111i−i−2i2iii−i−i00000−3300−i3i3−3300−i3−i3i3i3−3−3332-2−2i2i00000000−i3i300−3300000-1100i−i0000000
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χ522-22-22-12−2i2i1-2-12-2-21-22-12-11-21-12-111-2i−i−2i2i−2i2iii−i−i00i3i3−i3−i3-1-111i−i−2i2iii−i−i00000−3300−i3i33−300i3i3−i3−i333−3−3-222i−2i00000000−i3i300−33000001-100−ii0000000
χ532-2-2222200-2-2-2-2-2222-222222-2-2-2-22-2-200000000002i−2i2i−2i2i−2i2-22-20000000000000002i−2i0000002i−2i2i−2i000000002-200000000000000000002-200002i−2i000
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χ824-44-44-2-24i−4i22-2-2-4-4224-2-2122-1-2-21-122−2i2i−2i2i4i−4iii−i−i00−2i3−2i32i32i311-1-1−2i2i−2i2iii−i−i0000000000023−2300i3i3−i3−i3−3−333000000000000000000000000000000000000
χ834-44-44-2-24i−4i22-2-2-4-4224-2-2122-1-2-21-122−2i2i−2i2i4i−4iii−i−i002i32i3−2i3−2i311-1-1−2i2i−2i2iii−i−i00000000000−232300−i3−i3i3i333−3−3000000000000000000000000000000000000
χ844-44-44-2-2−4i4i22-2-2-4-4224-2-2122-1-2-21-1222i−2i2i−2i−4i4i−i−iii00−2i3−2i32i32i311-1-12i−2i2i−2i−i−iii00000000000−232300i3i3−i3−i333−3−3000000000000000000000000000000000000
χ854-44-44-2-2−4i4i22-2-2-4-4224-2-2122-1-2-21-1222i−2i2i−2i−4i4i−i−iii002i32i3−2i3−2i311-1-12i−2i2i−2i−i−iii0000000000023−2300−i3−i3i3i3−3−333000000000000000000000000000000000000
χ864-44-4-2444i−4i-4-44422-4-4-2-2-2422-4-2-24-4224i−4i4i−4i−2i2i4i4i−4i−4i000000-2-222−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000
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χ884-44-4-24-24i−4i-424-222-42-2-21-22-12-21-222-14i−4i−2i2i−2i2i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i00000000000000000000000000000000000003-3003i−3i0000000000000000
χ894-44-4-24-24i−4i-424-222-42-2-21-22-12-21-222-14i−4i−2i2i−2i2i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i0000000000000000000000000000000000000-3300−3i3i0000000000000000
χ904-44-4-24-2−4i4i-424-222-42-2-21-22-12-21-222-1−4i4i2i−2i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii00000000000000000000000000000000000003-300−3i3i0000000000000000
χ914-44-4-24-2−4i4i-424-222-42-2-21-22-12-21-222-1−4i4i2i−2i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii0000000000000000000000000000000000000-33003i−3i0000000000000000
χ924-44-4-2-244i−4i2-4-24222-4-21-2-2-1221-2-22-12−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i0000023−2300−2i32i3000000000000000000000000i3−i300−33000000000000000000
χ934-44-4-2-244i−4i2-4-24222-4-21-2-2-1221-2-22-12−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i00000−2323002i3−2i3000000000000000000000000−i3i3003−3000000000000000000
χ944-44-4-2-24−4i4i2-4-24222-4-21-2-2-1221-2-22-122i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii0000023−23002i3−2i3000000000000000000000000−i3i300−33000000000000000000
χ954-44-4-2-24−4i4i2-4-24222-4-21-2-2-1221-2-22-122i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii00000−232300−2i32i3000000000000000000000000i3−i3003−3000000000000000000
χ964-4-4444-200-42-42-444-2-44-2-24-22-422-2-4200000000004i−4i4i−4i4i−4i-22-22000000000000000−2i2i000000−2i2i−2i2i0000000000000000000000000000000000000000
χ974-4-4444-200-42-42-444-2-44-2-24-22-422-2-420000000000−4i4i−4i4i−4i4i-22-220000000000000002i−2i0000002i−2i2i−2i0000000000000000000000000000000000000000
χ984-4-444-24002-42-4-44-24-4-24-2-2422-42-22-400000000004i−4i−2i2i−2i2i-22-220000000000000004i−4i000000−2i2i−2i2i0000000000000000000000000000000000000000
χ994-4-444-24002-42-4-44-24-4-24-2-2422-42-22-40000000000−4i4i2i−2i2i−2i-22-22000000000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000000000
χ1004-4-444-2-2002222-44-2-2-4-2-21-2-2-122-11220000003i−3i−3i3i4i−4i−2i2i−2i2i1-11-100003i−3i−3i3i0000000−2i2i000000i−ii−i3-3-33000000000000000000000000000000000000
χ1014-4-444-2-2002222-44-2-2-4-2-21-2-2-122-11220000003i−3i−3i3i−4i4i2i−2i2i−2i1-11-100003i−3i−3i3i00000002i−2i000000−ii−ii-333-3000000000000000000000000000000000000
χ1024-4-444-2-2002222-44-2-2-4-2-21-2-2-122-1122000000−3i3i3i−3i4i−4i−2i2i−2i2i1-11-10000−3i3i3i−3i0000000−2i2i000000i−ii−i-333-3000000000000000000000000000000000000
χ1034-4-444-2-2002222-44-2-2-4-2-21-2-2-122-1122000000−3i3i3i−3i−4i4i2i−2i2i−2i1-11-10000−3i3i3i−3i00000002i−2i000000−ii−ii3-3-33000000000000000000000000000000000000
χ1044-4-44-24400-4-4-4-42-2442-2-24-2-2-422-44220000000000000000-22-22000000000000000000000000000000000004-40000000000000000000-22000000000
χ1054-4-44-24400-4-4-4-42-2442-2-24-2-2-422-44220000000000000000-22-2200000000000000000000000000000000000-4400000000000000000002-2000000000
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
χ10888-8-8-48-4008-4-84-44-844-42-44-2-44-244-4200000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4800-484-8-444-842-4-4-24-4-24442-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-400-4-444-44444222-2-22-2-2-2-2220000006-66-6000000-111-10000-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-4-444-44444222-2-22-2-2-2-222000000-66-66000000-111-100003-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-48i−8i44-4-44444-4222-2-2-2222-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-1-1112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4−8i8i44-4-44444-4222-2-2-2222-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-1-111−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-400-84-844-48-44-42-4-4244-24-44-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48004-84-84-4-4842-4-42-44-244-4-2400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044444-4-4-4422222-2-2-2-22-2-20000006i−6i−6i6i000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044444-4-4-4422222-2-2-2-22-2-2000000−6i6i6i−6i000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000

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