Finite Group Databasebeta

← Group #13168420

Character table — Group #13168420

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212224466661212121212121212121212124412121212666666121212121212121212122444412121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-11111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1111-1-111-1-11-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-11-1-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111111-11111-1-111-1-111-1-111-1-1-1-1-1-11111111-1-1-111-1-111-11-1-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1111-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111111111-1-1111111-1111-1-1-1-111-1-1-1-1111-1-1-11-1-111-1-11-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111111111-1-11111111-1-1-111-1-111-1-1-1-111-11-11-111-1-1-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-11-11111-1-1-1-1111-1-1-1-1-1-11111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-1111-11111-1-1-1-1-1-1111111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-11111-1-1111111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-11-1-1-1-11111111-1-1-1-1-1-111111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-11111-1-1-11-11-111-1-1-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-11111-1-11-1-1-11-1-111-1-11-1-11
χ17222222-1-12-1222-1222-1-122-1-1-1-12-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1220222-1-12200-1-10022000000002-1-1-1-1-10-1-1-100-1-10020020-1-10000-1000
χ18222222-1-12-1222-1222-1-122-1-1-1-12-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-202-2-2112200-1-1002200000000-2111110-1-1-100-1-100-200-201100001000
χ19222222-1-12-1222-1222-1-122-1-1-1-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1220-222-1-1-2-2001100-2-2000000002-1-1-1-1-10111001100-200-201100001000
χ20222222-1-12-1222-1222-1-122-1-1-1-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-20-2-2-211-2-2001100-2-200000000-211111011100110020020-1-10000-1000
χ21222222-1-12-1222-1222-1-1-22-1-1-1-12-12-1-2-22200-1-1-1-11-211-2-21111112-20-22211-2-200-1-1002200000000-2-1-1-11101-1-1001100200-20110000-1000
χ22222222-1-12-1222-1222-1-1-22-1-1-1-12-12-1-2-22200-1-1-1-11-211-2-2111111-220-2-2-2-1-1-2-200-1-10022000000002111-1-101-1-1001100-20020-1-100001000
χ23222222-1-12-1222-1222-1-1-22-1-1-1-12-12-1-2-2-2-200-1-1-1-11-211-2-21111112-202221122001100-2-200000000-2-1-1-1110-11100-1-100-20020-1-100001000
χ24222222-1-12-1222-1222-1-1-22-1-1-1-12-12-1-2-2-2-200-1-1-1-11-211-2-2111111-2202-2-2-1-122001100-2-2000000002111-1-10-11100-1-100200-20110000-1000
χ2522222-122-1222-12-12-12-12-12-1-1-1-12-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12220-1-122002200-1-10022000000-12-1-1-1-1-1000-1-100-1-10200200-1-1000-100
χ2622222-122-1222-12-12-12-12-12-1-1-1-12-12220022-1-1-1-12-1-1-1-1-122-1-1-1-1-2-22011-2-2002200-1-100220000001-21111-1000-1-100-1-10-200-20011000100
χ2722222-122-1222-12-12-12-12-12-1-1-1-12-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-122-20-1-12200-2-2001100-2-2000000-12-1-1-1-110001100110-200-20011000100
χ2822222-122-1222-12-12-12-12-12-1-1-1-12-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2011-2-200-2-2001100-2-20000001-2111110001100110200200-1-1000-100
χ2922222-122-1222-12-12-12-1-2-12-1-1-1-12-12-2-20022-1-1-1-1-211111-2-211112-2-20-1-1-2-2002200-1-100-2-200000012-1-11110001100-1-10-200200-1-1000100
χ3022222-122-1222-12-12-12-1-2-12-1-1-1-12-12-2-20022-1-1-1-1-211111-2-21111-22-201122002200-1-100-2-2000000-1-211-1-110001100-1-10200-20011000-100
χ3122222-122-1222-12-12-12-1-2-12-1-1-1-12-12-2-200-2-2-1-1-1-1-211111-2-211112-220-1-1-2-200-2-20011002200000012-1-111-1000-1-100110200-20011000-100
χ3222222-122-1222-12-12-12-1-2-12-1-1-1-12-12-2-200-2-2-1-1-1-1-211111-2-21111-2220112200-2-200110022000000-1-211-1-1-1000-1-100110-200200-1-1000100
χ332222-122222-1-1222-1-1-122-1-1222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-100220000-1-1-1-12222-1-1-1-122-1-1-1-100000022-1-1-1-1-1-1-1-1002000000-1-10000
χ342222-122222-1-1222-1-1-122-1-1222-1-1-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-100-220000-1-11122-2-2-1-111-2-21111000000-22-1-111-1-11100-2000000110000
χ352222-122222-1-1222-1-1-122-1-1222-1-1-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1002-2000011-1-1-2-22211-1-1-2-211110000002-211-1-111-1-100-2000000110000
χ362222-122222-1-1222-1-1-122-1-1222-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-100-2-200001111-2-2-2-2111122-1-1-1-1000000-2-211111111002000000-1-10000
χ372222-122222-1-1222-1-1-12-2-1-1222-1-1-1-1112222-1-1-1-1-2-2-2-21111111100-2-2000011-1-12222-1-11122-1-1-1-1000000-2-2-1-11111-1-100-2000000110000
χ382222-122222-1-1222-1-1-12-2-1-1222-1-1-1-11122-2-2-1-1-1-1-2-2-2-211111111002-20000111122-2-2-1-1-1-1-2-211110000002-2-1-1-1-11111002000000-1-10000
χ392222-122222-1-1222-1-1-12-2-1-1222-1-1-1-111-2-222-1-1-1-1-2-2-2-21111111100-220000-1-1-1-1-2-2221111-2-21111000000-221111-1-1-1-1002000000-1-10000
χ402222-122222-1-1222-1-1-12-2-1-1222-1-1-1-111-2-2-2-2-1-1-1-1-2-2-2-21111111100220000-1-111-2-2-2-211-1-122-1-1-1-10000002211-1-1-1-11100-2000000110000
χ412-22-2222-22-2-2-2-22-222220-2-22-2-222-2-2002-22i−2i22-2-200000000000000000000002i−2i2-22i−2i2-2002i−2i2i2i−2i−2i000000002-200002i−2i000000000000000
χ422-22-2222-22-2-2-2-22-222220-2-22-2-222-2-2002-2−2i2i22-2-20000000000000000000000−2i2i2-2−2i2i2-200−2i2i−2i−2i2i2i000000002-20000−2i2i000000000000000
χ432-22-2222-22-2-2-2-22-222220-2-22-2-222-2-200-222i−2i22-2-200000000000000000000002i−2i-222i−2i-2200−2i2i−2i−2i2i2i00000000-2200002i−2i000000000000000
χ442-22-2222-22-2-2-2-22-222220-2-22-2-222-2-200-22−2i2i22-2-20000000000000000000000−2i2i-22−2i2i-22002i−2i2i2i−2i−2i00000000-220000−2i2i000000000000000
χ452-22-2-122-22-211-22-2-1-1-120112-2-2-1-1113−32-22i−2i-1-11100003−33−333−3−3000000003−3−ii2-22i−2i-11−i3i32i−2i−i−iii00000000-11−i3i33−3−ii000000000−i3i30000
χ462-22-2-122-22-211-22-2-1-1-120112-2-2-1-1113−32-2−2i2i-1-11100003−33−333−3−3000000003−3i−i2-2−2i2i-11i3−i3−2i2iii−i−i00000000-11i3−i33−3i−i000000000i3−i30000
χ472-22-2-122-22-211-22-2-1-1-120112-2-2-1-1113−3-222i−2i-1-11100003−33−333−3−300000000−33−ii-222i−2i1-1−i3i3−2i2iii−i−i000000001-1−i3i3−33−ii000000000i3−i30000
χ482-22-2-122-22-211-22-2-1-1-120112-2-2-1-1113−3-22−2i2i-1-11100003−33−333−3−300000000−33i−i-22−2i2i1-1i3−i32i−2i−i−iii000000001-1i3−i3−33i−i000000000−i3i30000
χ492-22-2-122-22-211-22-2-1-1-120112-2-2-1-111−332-22i−2i-1-1110000−33−33−3−33300000000−33−ii2-22i−2i-11i3−i32i−2i−i−iii00000000-11i3−i3−33−ii000000000i3−i30000
χ502-22-2-122-22-211-22-2-1-1-120112-2-2-1-111−332-2−2i2i-1-1110000−33−33−3−33300000000−33i−i2-2−2i2i-11−i3i3−2i2iii−i−i00000000-11−i3i3−33i−i000000000−i3i30000
χ512-22-2-122-22-211-22-2-1-1-120112-2-2-1-111−33-222i−2i-1-1110000−33−33−3−333000000003−3−ii-222i−2i1-1i3−i3−2i2iii−i−i000000001-1i3−i33−3−ii000000000−i3i30000
χ522-22-2-122-22-211-22-2-1-1-120112-2-2-1-111−33-22−2i2i-1-1110000−33−33−3−333000000003−3i−i-22−2i2i1-1−i3i32i−2i−i−iii000000001-1−i3i33−3i−i000000000i3−i30000
χ5344444-2-2-2-2-244-2-2-24-2-214-2-2111-2-2-2-24400001111-2-211-2-2-2-211114400-2-2-2-2000000000000000000-2-211110000000000000000000000000
χ5444444-2-2-2-2-244-2-2-24-2-214-2-2111-2-2-2-24400001111-2-211-2-2-2-21111-4-400222200000000000000000022-1-1-1-10000000000000000000000000
χ5544444-2-2-2-2-244-2-2-24-2-21-4-2-2111-2-2-2-2-4-40000111122-1-12222-1-1-1-14-400-2-2220000000000000000002-211-1-10000000000000000000000000
χ5644444-2-2-2-2-244-2-2-24-2-21-4-2-2111-2-2-2-2-4-40000111122-1-12222-1-1-1-1-440022-2-2000000000000000000-22-1-1110000000000000000000000000
χ574444-24-2-24-2-2-24-24-2-21-24-21-2-2-2-21-21-2-244001111-24-2-2-2-211111100040000-2-200-2-200-2-2000000000000000-211001100000000000000000
χ584444-24-2-24-2-2-24-24-2-21-24-21-2-2-2-21-21-2-2-4-4001111-24-2-2-2-2111111000-4000022002200220000000000000002-1-100-1-100000000000000000
χ594444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-2-21-2122440011112-42222-1-1-1-1-1-1000-400002200-2-200-2-200000000000000021100-1-100000000000000000
χ604444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-2-21-2122-4-40011112-42222-1-1-1-1-1-100040000-2-200220022000000000000000-2-1-1001100000000000000000
χ614444-2-244-24-2-2-24-2-21-2-241-2-2-2-21-21-2-2-2004411114-2-2-211-2-211110040000000-2-200-2-200-2-2000000000000-2000110011000000000000000
χ624444-2-244-24-2-2-24-2-21-2-241-2-2-2-21-21-2-2-200-4-411114-2-2-211-2-2111100-4000000022002200220000000000002000-1-100-1-1000000000000000
χ634444-2-244-24-2-2-24-2-21-2-2-41-2-2-2-21-21-22200441111-4222-1-122-1-1-1-100-40000000-2-200-2-200220000000000002000-1-10011000000000000000
χ644444-2-244-24-2-2-24-2-21-2-2-41-2-2-2-21-21-22200-4-41111-4222-1-122-1-1-1-1004000000022002200-2-2000000000000-20001100-1-1000000000000000
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χ784-44-4-24-224222-4-2-4-2-21-202-1-222-212-1−23234-40011-1-10000−23233−333−3−300000000−232300-2200-2200000000000000001-1003−300000000000000000
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χ834-44-4-2-24-4-2-422242-21-2-20-12-2221-2-12−232300−4i4i11-1-100003−3−232333−3−300000000002i−2i002i−2i00−2i32i30000000000000000i3−i300−ii000000000000000
χ844-4-44444-4-444-4-4-44-44440-4-4-4-44-4-4440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-22-4-24-4-424-44-2-20-4222-2-424-2000000-222-2000000000000000000−2i32i30000000000000000000000−2i32i30000000000000000000000000
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χ884-4-444-24-4244-42-4-2-4-24-202-422-22-4-24000000-222-200000000000000002i3−2i300000000000000000000002i3−2i3000000000000000000000000000
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χ914-4-444-2-222-24-422-2-4-2-21022-1-1122-2-20000001-1-1100-330000-33-330000−2i32i32i3−2i300000000000000000000i3−i3−i3i30000000000000000000000000
χ924-4-444-2-222-24-422-2-4-2-21022-1-1122-2-20000001-1-1100-330000-33-3300002i3−2i3−2i32i300000000000000000000−i3i3i3−i30000000000000000000000000
χ934-4-44-244-4-44-22-4-442-2-24022-4-4422-2-2000000-222-2000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ944-4-44-244-4-44-22-4-442-2-24022-4-4422-2-2000000-222-20000000000000000000000000000000000−232323−230000000000000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-444-88-444-8-4-420-4-4-22-244440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-4-844-484-84-42-40-424-444-24-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4884-84-4-4-8442-4-402-44-44-24-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4444-4-4444222022-22-2-2-2-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4444-4-4444222022-22-2-2-2-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-44-44-8-84-448-4-420442-2-2-4-44400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-44444-44-42220-2-22-2-222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-44444-44-42220-2-22-2-222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-8-4-44-8484-42-404-244-44-2-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-848-444-8-442-4-40-2444-4-242-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-4-4444-442220-2-2-2-22-2-222000000-111-1006-60000-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-4-4444-442220-2-2-2-22-2-222000000-111-100-6600003-33-3000000000000000000000000000000000000000000000000000000000

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