Finite Group Databasebeta

← Group #13169345

Character table — Group #13169345

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212244466666666121212121212121212121212121244121212121212121212121212244441212121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1111111111111111-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111-1-11-111-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-11-1-11-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-111111111111111111111-1111111111111-1-1-1-1-1-1111111-1-1-11111111-1-1-1-1-11-1-11-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11111111-1-1-1-1-1-11-1-1-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-11-1-11111-1-1-11-11-11111-1-1-1-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111111111-111-111-1-111-1-11-1-1-11-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111-1-111-11-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1111-1-1-1-1-1-1111-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-1-11-1-111-1-111111-1-1-1-1-1-1111-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-111-1-1-1-111-1-111111-1-111-11-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-11111111111-1-1-1-111-1-1-1-1-1-1111-1-11-1-111-1-1111-1-1-11-1-111-1-111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111111111-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11-11-11111-1-1-1-111-1
χ17222222-122-12-12-122-1-122-1-122-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1022200000000-1-122-1-12200000000-12-12-1-1-1-1-1-1-1-120020-1-10000-10000
χ18222222-122-12-12-122-1-122-1-122-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-102-2-2000000001122-1-12200000000-1-21-21111-1-1-1-1-200-2011000010000
χ19222222-122-12-12-122-1-122-1-122-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-22200000000-1-1-2-211-2-20000000012-12-1-1-1-11111-200-2011000010000
χ20222222-122-12-12-122-1-122-1-122-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-20000000011-2-211-2-2000000001-21-21111111120020-1-10000-10000
χ21222222-122-12-12-122-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-22-200000000-1-122-1-1-2-2000000001-21211-1-1-1-111-20020-1-1000010000
χ22222222-122-12-12-122-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-2-22000000001122-1-1-2-20000000012-1-2-1-111-1-111200-20110000-10000
χ23222222-122-12-12-122-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111022-200000000-1-1-2-2112200000000-1-21211-1-111-1-1200-20110000-10000
χ24222222-122-12-12-122-1-12-2-1-122-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111102-220000000011-2-2112200000000-12-1-2-1-11111-1-1-20020-1-1000010000
χ2522222-122-12-12222-12-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1220022-1-1-1-1-1-100-1-122-1-122-1-1-1-12220000000-1-1-1-10020000-1-1-1-100000
χ2622222-122-12-12222-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-2-21111-1-1-1-12-1-122-1-1-1-1-2200-2-211111100-1-122-1-1-2-21111-2-220000000-1-1-1-100-20000111100000
χ2722222-122-12-12222-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-12-20022-1-1-1-1-1-10011-2-21122-1-1-1-1-2-2-20000000111100-20000111100000
χ2822222-122-12-12222-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-2-200-2-21111110011-2-211-2-2111122-2000000011110020000-1-1-1-100000
χ2922222-122-12-12222-12-1-1-22-1-1-1-122-1-111-2-211112222-1-1-1-1-1-1-1-1-211-2-21111-2-200-2-211111100-1-1221122-1-1-1-122-20000000-1-11100-20000-1-11100000
χ3022222-122-12-12222-12-1-1-22-1-1-1-122-1-111-2-2111122-2-21111-1-1-1-1-211-2-211112-20022-1-1-1-1-1-100-1-12211-2-21111-2-2-20000000-1-111002000011-1-100000
χ3122222-122-12-12222-12-1-1-22-1-1-1-122-1-111-2-21111-2-222-1-1-1-1-1-1-1-1-211-2-21111-2200-2-21111110011-2-2-1-122-1-1-1-1-2-22000000011-1-1002000011-1-100000
χ3222222-122-12-12222-12-1-1-22-1-1-1-122-1-111-2-21111-2-2-2-21111-1-1-1-1-211-2-21111220022-1-1-1-1-1-10011-2-2-1-1-2-21111222000000011-1-100-20000-1-11100000
χ332222-122-12222-12-12-12-12-12-1-12-1-1-1222-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-12022-1-122-1-1-1-122000000-1-1-1-1-1-1000-12-1-1-1-1-10000020020000000-1-100
χ342222-122-12222-12-12-12-12-12-1-12-1-1-1222-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-120-2-2-1-122-1-1-1-1-2-2000000-1-1-1-1-1-10001-21111100000-200-200000001100
χ352222-122-12222-12-12-12-12-12-1-12-1-1-1222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-202211-2-2111122000000111111000-12-1-1-1-1-100000-200-200000001100
χ362222-122-12222-12-12-12-12-12-1-12-1-1-1222-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-211-2-21111-2-20000001111110001-2111110000020020000000-1-100
χ372222-122-12222-12-12-12-1-2-12-1-12-1-1-12-2-211111100222222-1-1-1-1-2-2-2111111-202-211-2-2111122000000-1-1-1-1-1-10001-2-111-1-100000200-200000001-100
χ382222-122-12222-12-12-12-1-2-12-1-12-1-1-12-2-211111100222222-1-1-1-1-2-2-2111111-20-2211-2-21111-2-2000000-1-1-1-1-1-1000-121-1-11100000-20020000000-1100
χ392222-122-12222-12-12-12-1-2-12-1-12-1-1-12-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-2111111202-2-1-122-1-1-1-1220000001111110001-2-111-1-100000-20020000000-1100
χ402222-122-12222-12-12-12-1-2-12-1-12-1-1-12-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-211111120-22-1-122-1-1-1-1-2-2000000111111000-121-1-11100000200-200000001-100
χ412-22-2222-222-2-2-2-22-22220-2-2-2-22-222-2000000002i−2i2-222-2-22-2-22000000000000000000000002i−2i2i−2i002-222-2-22i−2i000000002i−2i0000000002i−2i0000000
χ422-22-2222-222-2-2-2-22-22220-2-2-2-22-222-2000000002i−2i-22-2-2222-2-22000000000000000000000002i−2i2i−2i00-22-2-222−2i2i000000002i−2i000000000−2i2i0000000
χ432-22-2222-222-2-2-2-22-22220-2-2-2-22-222-200000000−2i2i2-222-2-22-2-2200000000000000000000000−2i2i−2i2i002-222-2-2−2i2i00000000−2i2i000000000−2i2i0000000
χ442-22-2222-222-2-2-2-22-22220-2-2-2-22-222-200000000−2i2i-22-2-2222-2-2200000000000000000000000−2i2i−2i2i00-22-2-2222i−2i00000000−2i2i0000000002i−2i0000000
χ452-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11−i3i300−i3−i3i3i32i−2i2-2-1-111-111-10−i3i300−i3−i3i3i3000000−i3i3−i3−i3i3i300−ii2i−2i3−32-2-1-1112i−2i00000000−ii3−30000000−ii3−300000
χ462-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11−i3i300−i3−i3i3i32i−2i-2211-1-1-111-10−i3i300−i3−i3i3i3000000i3−i3i3i3−i3−i300−ii2i−2i3−3-2211-1-1−2i2i00000000−ii3−30000000i−i−3300000
χ472-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11−i3i300−i3−i3i3i3−2i2i2-2-1-111-111-10−i3i300−i3−i3i3i3000000−i3i3−i3−i3i3i300i−i−2i2i−332-2-1-111−2i2i00000000i−i−330000000i−i−3300000
χ482-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11−i3i300−i3−i3i3i3−2i2i-2211-1-1-111-10−i3i300−i3−i3i3i3000000i3−i3i3i3−i3−i300i−i−2i2i−33-2211-1-12i−2i00000000i−i−330000000−ii3−300000
χ492-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11i3−i300i3i3−i3−i32i−2i2-2-1-111-111-10i3−i300i3i3−i3−i3000000i3−i3i3i3−i3−i300−ii2i−2i−332-2-1-1112i−2i00000000−ii−330000000−ii−3300000
χ502-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11i3−i300i3i3−i3−i32i−2i-2211-1-1-111-10i3−i300i3i3−i3−i3000000−i3i3−i3−i3i3i300−ii2i−2i−33-2211-1-1−2i2i00000000−ii−330000000i−i3−300000
χ512-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11i3−i300i3i3−i3−i3−2i2i2-2-1-111-111-10i3−i300i3i3−i3−i3000000i3−i3i3i3−i3−i300i−i−2i2i3−32-2-1-111−2i2i00000000i−i3−30000000i−i3−300000
χ522-22-22-12-2-121-2-2-2212-1-10-2111-1-22-11i3−i300i3i3−i3−i3−2i2i-2211-1-1-111-10i3−i300i3i3−i3−i3000000−i3i3−i3−i3i3i300i−i−2i2i3−3-2211-1-12i−2i00000000i−i3−30000000−ii−3300000
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χ5544444-2-24-2-2-2-24-24-2-21-2-4-21-2-21-2-2-2122-4-422224400000011112-1-122-1-1-1-10-4000000000000-2-2-2-222000000002000000011-1-10000000000000000
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χ764-44-444-2-44-2-42-424-4-2-24022-4-4-22-242000000004i−4i000000-222-2000000000000000000000004i−4i−2i2i000000000000000000−2i2i000000000000000000
χ774-44-444-2-44-2-42-424-4-2-24022-4-4-22-24200000000−4i4i000000-222-200000000000000000000000−4i4i2i−2i0000000000000000002i−2i000000000000000000
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χ804-44-44-2-2-4-2-222-4242-21-202-12212-2-2-12i3−2i3002i32i3−2i3−2i34i−4i0000001-1-110−i3i300−i3−i3i3i300000000000000−2i2i−2i2i−23230000000000000000i−i3−30000000000000000
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χ824-44-4-244244-4-42-4-2-4-24-202-42242-2-2-400000000004-444-4-4-222-200000000000000000000000000000-22-2-222000000000000000000000000000000
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χ844-44-4-2-242-242-42-4-22-2-21022-1-1-22-212−2i32i300i3i3−i3−i3004-4-2-2221-1-110−2i32i300i3i3−i3−i3000000−2i32i3i3i3−i3−i300000000-2211-1-1000000000000000000000000000000
χ854-44-4-2-242-242-42-4-22-2-21022-1-1-22-212−2i32i300i3i3−i3−i300-4422-2-21-1-110−2i32i300i3i3−i3−i30000002i3−2i3−i3−i3i3i3000000002-2-1-111000000000000000000000000000000
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χ874-44-4-2-242-242-42-4-22-2-21022-1-1-22-2122i3−2i300−i3−i3i3i300-4422-2-21-1-1102i3−2i300−i3−i3i3i3000000−2i32i3i3i3−i3−i3000000002-2-1-111000000000000000000000000000000
χ884-4-44444-4-4-4-4-444-444440-44-44-44-4-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
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χ994-4-44-2-2422-42-4-242-2-2-2102-2-112-22-120023−23−333−3000023−23−23231-11-100023−23−333−3000000003-3-330000000000−333−3000000000000000000000000000000
χ1004-4-44-2-2422-42-4-242-2-2-2102-2-112-22-120023−23−333−30000−232323−231-11-100023−23−333−300000000-333-300000000003−3−33000000000000000000000000000000
χ1014-4-44-2-2422-42-4-242-2-2-2102-2-112-22-1200−23233−3−33000023−23−23231-11-1000−23233−3−3300000000-333-30000000000−333−3000000000000000000000000000000
χ1024-4-44-2-2422-42-4-242-2-2-2102-2-112-22-1200−23233−3−330000−232323−231-11-1000−23233−3−33000000003-3-3300000000003−3−33000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
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χ10588-8-88-4-4844-4-4-84-84-42-40-4-2-44-24442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-48-4-4-848-4444-82-4-4024-444-2-24-4000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-444-4-4444422202-22-2-2-2-2-2200006i−6i6i−6i00000000-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-4-444-4-4444422202-22-2-2-2-2-220000−6i6i−6i6i00000000-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-448-4-8444-4-82-4-40-2444-4-22-4400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4-44444-442220-2-2-2-22-222-2−4i34i3002i32i3−2i3−2i300000000-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-4-44444-442220-2-2-2-22-222-24i3−4i300−2i3−2i32i32i300000000-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-844448-4-8-4-42-40424-4-2-444-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444444-4-44-42220-22-22-22-2-2-20043−43−232323−2300000000-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444444-4-44-42220-22-22-22-2-2-200−434323−23−232300000000-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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