Finite Group Databasebeta

← Group #13169266

Character table — Group #13169266

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212441212121212121212121212121212121212121212222446666121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1-1-1111111111111-1-1111111-11-11-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-1111-111111111-1-1-1-1-11-11-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-1-1-111111111-1-1-1-1-1-11-1111111-1-1-1-11111-1-11-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11-11-1-1-1-1-1111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-111-1-11111111-1-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111111111-1-11-111-1-111-1-111-1-1-111-1-1-1-111-1-11-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-1111-111-1111111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1111-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-111-111-1-1-1-11111-1-11-111-1111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-111111111-11-1-111-1-111-1-111-111-1-1-1-111-1-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-111-1-111111111-111111-1-1-1-111-1-111-1-1-111-1-1-1-111-11-11
χ17222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-120200022-1-1-1-1-1-1-1-1220022-1-1-1-102020000-1-1-1-1-1-1-1-120000-1-100000000
χ18222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-120-200022-1-1-1-11111-2-200-2-21111020-20000-1-1-1-11111-200001100000000
χ19222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-202000-2-21111-1-1-1-12200-2-211110-20200001111-1-1-1-1-200001100000000
χ20222222-12222-1-1-1222-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-20-2000-2-211111111-2-20022-1-1-1-10-20-200001111111120000-1-100000000
χ21222222-12222-1-1-1222-1-1-22-1-1-1-122-1-1112222-1-1-1-1-2-21111-2-21111-20-200022-1-111-1-111220022-1-1-1-10-20-20000-1-111-1-111-200001100000000
χ22222222-12222-1-1-1222-1-1-22-1-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-21111-20200022-1-11111-1-1-2-200-2-211110-2020000-1-11111-1-120000-1-100000000
χ23222222-12222-1-1-1222-1-1-22-1-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-2111120-2000-2-211-1-1-1-1112200-2-21111020-2000011-1-1-1-11120000-1-100000000
χ24222222-12222-1-1-1222-1-1-22-1-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-21111202000-2-211-1-111-1-1-2-20022-1-1-1-10202000011-1-111-1-1-200001100000000
χ2522222-1222-1-1222-12-12-12-12-12-1-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12202-1-1-1-12222000000220000002-1-10-1-1-1-1-1-1-1-10000020200000-1-1-1000
χ2622222-1222-1-1222-12-12-12-12-12-1-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12-20-211-1-12222000000-2-2000000-2-1101111-1-1-1-100000-20-200000111000
χ2722222-1222-1-1222-12-12-12-12-12-1-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2202-1-111-2-2-2-20000002200000021-10-1-1-1-1111100000-20-200000111000
χ2822222-1222-1-1222-12-12-12-12-12-1-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-21111-2-2-2-2000000-2-2000000-2110111111110000020200000-1-1-1000
χ2922222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-22200-1-1-1-1-21-2-211111111-220-2-1-1-1-122-2-2000000-2-2000000211011-1-1-1-11100000-20200000-1-11000
χ3022222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-22200-1-1-1-1-21-2-211111111-2-20211-1-122-2-200000022000000-21-10-1-111-1-1110000020-20000011-1000
χ3122222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-2-2-200-1-1-1-1-21-2-211111111220-2-1-111-2-222000000-2-20000002-11011-1-111-1-10000020-20000011-1000
χ3222222-1222-1-1222-12-12-1-2-12-12-1-1-12-1-2-2-2-200-1-1-1-1-21-2-2111111112-2021111-2-22200000022000000-2-1-10-1-11111-1-100000-20200000-1-11000
χ332222-122-1-1222222-1-1-122-1-12-12-1-1-12220022-1-1-1-1-12-1-122-1-1-1-1-1-10222220000002222-1-1-1-1000000-102-1-1-1-1-10000-1-1-1-10020200-1-1000-100
χ342222-122-1-1222222-1-1-122-1-12-12-1-1-12220022-1-1-1-1-12-1-122-1-1-1-1-1-10-22-2-2-20000002222-1-11100000010-2-111110000-1-1-1-100-20-20011000100
χ352222-122-1-1222222-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-102-2222000000-2-2-2-211-1-1000000-1021-1-1-1-10000111100-20-20011000100
χ362222-122-1-1222222-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-2-2-2000000-2-2-2-2111100000010-211111000011110020200-1-1000-100
χ372222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-11-211-2-211111102-2-22200000022-2-2-1-111000000-10-2111-1-10000-1-11100-2020011000-100
χ382222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-11-211-2-21111110-2-22-2-200000022-2-2-1-1-1-10000001021-1-1110000-1-1110020-200-1-1000100
χ392222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-11-211-2-2111111022-222000000-2-2221111000000-10-2-111-1-1000011-1-10020-200-1-1000100
χ402222-122-1-1222222-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-11-211-2-21111110-222-2-2000000-2-22211-1-1000000102-1-1-111000011-1-100-2020011000-100
χ412-22-2222-222-2-2-22-2-22220-2-2-222-22-2-2002i−2i2i−2i2-2-220000000000000000002i−2i2i−2i002i−2i002i−2i002-222-2-2000000002i−2i002i−2i00000000000000000
χ422-22-2222-222-2-2-22-2-22220-2-2-222-22-2-2002i−2i−2i2i2-2-220000000000000000002i−2i2i−2i00−2i2i00−2i2i00-22-2-222000000002i−2i00−2i2i00000000000000000
χ432-22-2222-222-2-2-22-2-22220-2-2-222-22-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i−2i2i002i−2i002i−2i00-22-2-22200000000−2i2i002i−2i00000000000000000
χ442-22-2222-222-2-2-22-2-22220-2-2-222-22-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i−2i2i00−2i2i00−2i2i002-222-2-200000000−2i2i00−2i2i00000000000000000
χ452-22-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i30000002i−2i−ii3−3−ii3−32i−2i002-2-1-11100000000−ii3−3−ii3−300000−i3i300000000
χ462-22-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i30000002i−2i−ii3−3i−i−33−2i2i00-2211-1-100000000−ii3−3i−i−3300000i3−i300000000
χ472-22-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000−2i2ii−i−33−ii3−32i−2i00-2211-1-100000000i−i−33−ii3−300000i3−i300000000
χ482-22-222-1-222-211-1-2-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000−2i2ii−i−33i−i−33−2i2i002-2-1-11100000000i−i−33i−i−3300000−i3i300000000
χ492-22-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i30000002i−2i−ii−33−ii−332i−2i002-2-1-11100000000−ii−33−ii−3300000i3−i300000000
χ502-22-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i30000002i−2i−ii−33i−i3−3−2i2i00-2211-1-100000000−ii−33i−i3−300000−i3i300000000
χ512-22-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000−2i2ii−i3−3−ii−332i−2i00-2211-1-100000000i−i3−3−ii−3300000−i3i300000000
χ522-22-222-1-222-211-1-2-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000−2i2ii−i3−3i−i3−3−2i2i002-2-1-11100000000i−i3−3i−i3−300000i3−i300000000
χ5344444-2-244-2-2-2-2-2-24-2-214-2-21-21-2-2-21-2-2440011114-2-2-211-2-21111400000-2-2-2-2-2-2000000000000000-200000011110000000000000000000
χ5444444-2-244-2-2-2-2-2-24-2-214-2-21-21-2-2-21-2-2-4-40011114-2-2-211-2-21111-4000002222220000000000000002000000-1-1-1-10000000000000000000
χ5544444-2-244-2-2-2-2-2-24-2-21-4-2-21-21-2-2-212244001111-4222-1-122-1-1-1-1-400000-2-2-2-222000000000000000200000011-1-10000000000000000000
χ5644444-2-244-2-2-2-2-2-24-2-21-4-2-21-21-2-2-2122-4-4001111-4222-1-122-1-1-1-14000002222-2-2000000000000000-2000000-1-1110000000000000000000
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χ584444-24-2-2-244-2-2-24-2-21-24-21-21-2-2-21-2-2-200-4-41111-2411-2-2-2-2111100-400000000022222200000000000200000000-1-1-1-1000000000000000
χ594444-24-2-2-244-2-2-24-2-21-2-4-21-21-2-2-21-222004411112-4-1-12222-1-1-1-100-4000000000-2-222-2-20000000000020000000011-1-1000000000000000
χ604444-24-2-2-244-2-2-24-2-21-2-4-21-21-2-2-21-22200-4-411112-4-1-12222-1-1-1-100400000000022-2-22200000000000-200000000-1-111000000000000000
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χ634444-2-24-2-2-2-2444-2-21-2-2-41-2-2-2-211-2-2-4-400001111222222-1-1-1-1-1-1040-4-2-200000000000022000000-2020-1-11100000000000000000000000
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χ814-44-4-24-22-24-422-2-42-21-202-121-22-2-12−2i32i300−4i4i1-1-1100i3−i3−2i32i300i3i3−i3−i30000000000002i−2i−23232i−2i00000000000000000000−ii3−3000000000000000
χ824-44-4-24-22-24-422-2-42-21-202-121-22-2-122i3−2i3004i−4i1-1-1100−i3i32i3−2i300−i3−i3i3i3000000000000−2i2i−2323−2i2i00000000000000000000i−i3−3000000000000000
χ834-44-4-24-22-24-422-2-42-21-202-121-22-2-122i3−2i300−4i4i1-1-1100−i3i32i3−2i300−i3−i3i3i30000000000002i−2i23−232i−2i00000000000000000000−ii−33000000000000000
χ844-4-44444-4-4-4-4-44-4444440-4-44-4-44-44-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-2-4-4-4-42-22444-2-20-42-2224-4-22000000-22-22000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ864-4-4444-2-4-4-4-42-22444-2-20-42-2224-4-22000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
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χ894-4-44-24422-4-4-44-44-2-2-2402242-4-22-2-4000000-22-22000000000000000000000000000000−2i32i30000000000−2i32i30000000000000000000000000
χ904-4-44-24422-4-4-44-44-2-2-2402242-4-22-2-4000000-22-220000000000000000000000000000002i3−2i300000000002i3−2i30000000000000000000000000
χ914-4-44-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-10000003i−3i3i−3i3i−3i000023−23000000000000−2i32i30000000000i3−i3−3300000000000000000000000
χ924-4-44-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-10000003i−3i3i−3i3i−3i0000−23230000000000002i3−2i30000000000−i3i33−300000000000000000000000
χ934-4-44-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-1000000−3i3i−3i3i−3i3i000023−230000000000002i3−2i30000000000−i3i3−3300000000000000000000000
χ944-4-44-2-242222-44-4-2-21-2-20-12-2221-1-220000001-11-1000000−3i3i−3i3i−3i3i0000−2323000000000000−2i32i30000000000i3−i33−300000000000000000000000
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
χ9788-8-88-4-48-84-4-4444-8-4-420-4-4-24-2444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-44-88-444-84-42-40-424-2444-2-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-48-444-48-8-8442-4-402-4444-2-24-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-444-4-44444222022-2-2-2-2-2-22000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-444-4-44444222022-2-2-2-2-2-22000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-484-4-44-8-88442-4-40-244-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-4-4444-4442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-4-4444-4442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4-8-8444-44-48-4-4204424-2-44-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-444-8-84-448-4-42-404-2-4-24-44240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-44-4-42220-2-22-2-22-22-2000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-44-4-42220-2-22-2-22-22-2000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000

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