Finite Group Databasebeta

← Group #13172179

Character table — Group #13172179

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666662333666666666666666664444121212123666666666666444412121212121212121212121212121212121212121212221212121212121212121212122444466121212126121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111-1-111111111111111111111-1-11-11111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111-1111-1-11111-1-1-1-1111111111111-1-111-11-1-1-1-111111-1-11-1-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-1-11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-11-1-1-1-111-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1-11-1-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-11-1-1-11111-1-1-1-1-111
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
χ91111111111111111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1111-1-1-1-1-11-1-1-1-111-1-1111111-1-11111-1-1-1-1111-1-1-111-1-111-1-11-11-1-111-1-1111-1-1-11
χ101111111111111111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-11-1111-1-1-1-111-1-1-11111-1-1-1-1-1111-1
χ111111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-111111-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-1-1-11111-1-111-1-11-1-111-1-111-11-1
χ121111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-111111-1-1-1-1-1111-1-1-1-11-11-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1111-1-111-1-111-1111-1-1-11111-1-11-11
χ131111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-11-11-1-111111111-1-111-1-1-1-11111-1-11-1-1-111-1-111-1-1-1111-1-1-11111-1-111-1
χ141111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-11-1111-1-1-1-11111-1-11-1-111-1-111-1-11
χ151111111111111111-1111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-111-11111111-1-1-1-1-1-111-1-1-1-11111111-11-1-1-11111-1-1-1-1-11111-1-1-1-1-111-11
χ161111111111111111-1111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-111-1-1-1-1111111-1111-1-111-1-1111-11-1-111-1-1111-1-11-1
χ17222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1-12002-1-100-1-1-1-1222222-1-1-1-1-1-1-1-1220020-1-1-1-1000002000-1-1-1-10000000
χ18222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-20021100-1-111-2-22222-1-1-1-1-1-1-1-1-2-200-20111100000-200011110000000
χ19222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2221111-1222-1-1-1-1-1-1-1-1-1200-2-1-10011-1-122-2-2-2-211111111-2-20020-1-1-1-100000-200011110000000
χ20222222-122-12-1-122222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-21111-1222-1-1-1-1-1-1-1-1-1-200-211001111-2-2-2-2-2-2111111112200-201111000002000-1-1-1-10000000
χ21222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-12222-1-1-1-1-1-2-2-211-1-1-11111-200-2110011-1-12222-2-2-1-1-1-111112200-20-1-11100000-2000-1-1110000000
χ22222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-122-2-2-1-1-1-1-1-2-2-211-1-1-11111200-2-1-1001111-2-222-2-2-1-1-1-11111-2-2002011-1-100000200011-1-10000000
χ23222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-1-2-2221111-1-2-2-211-1-1-11111-20021100-1-1-1-122-2-2221111-1-1-1-1-2-200-20-1-11100000200011-1-10000000
χ24222222-122-12-1-1222-22-1-1-2-2112-1-1-1111122-1-1-1-2-2-2-21111-1-2-2-211-1-1-111112002-1-100-1-111-2-2-2-2221111-1-1-1-122002011-1-100000-2000-1-1110000000
χ2522222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-122002222-12-1-122-1-1-1-1-1-1-102220022220000-1-1-1-1-1-1-1-1-1-1-1-100-1-1020000-1-1-1-120020000000-10-100
χ2622222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-122002222-12-1-122-1-1-1-1-1-1-10-2-2200-2-2220000-1-1-1-1-1-1-1-1-1-1-1-100110-200001111-200-2000000010100
χ2722222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-1-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-1022-20022-2-2000011111111111100-1-1020000-1-1-1-1-200-2000000010100
χ2822222-12-1-1222222-12-12-1-1-122-12-1-1-1-1-1-1-1-122-1-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-10-2-2-200-2-2-2-2000011111111111100110-20000111120020000000-10-100
χ2922222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-122002222-1-211-2-2-1-1-1111102-2-20022-2-20000-1-111-1-1-1-1111100-110-20000-1-111200-20000000-10100
χ3022222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-122002222-1-211-2-2-1-1-111110-22-200-2-2-2-20000-1-111-1-1-1-11111001-102000011-1-1-2002000000010-100
χ3122222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-1-2-200-2-2-2-2-1-211-2-2-1-1-1111102-22002222000011-1-11111-1-1-1-100-110-20000-1-111-2002000000010-100
χ3222222-12-1-1222222-1-2-12-111-2-2-12-1-11111-1-122-1-2-200-2-2-2-2-1-211-2-2-1-1-111110-22200-2-222000011-1-11111-1-1-1-1001-102000011-1-1200-20000000-10100
χ332222-122222-122-1-122-1-122222-1-1222222-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1222022-1-10022-1-10000000000000022-1-1-1-1-1-1-1-1-1-1002020000-1-10-1000
χ342222-122222-122-1-122-1-122222-1-1222222-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2022110022-1-100000000000000-2-2-11-1-1-1-1111100-20-200001101000
χ352222-122222-122-1-122-1-122222-1-1222222-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2220-2-2-1-100-2-21100000000000000221-11111-1-1-1-100-20-200001101000
χ362222-122222-122-1-122-1-122222-1-1222222-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20-2-21100-2-21100000000000000-2-21111111111002020000-1-10-1000
χ372222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-1200220000-111111-1-1-11111-22-20-2-2-1-10022-1-1000000000000002-211-1-111-1-1110020-20000-1-101000
χ382222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-1200220000-111111-1-1-11111-2-220-2-2110022-1-100000000000000-221-1-1-11111-1-100-2020000110-1000
χ392222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-1200-2-20000-111111-1-1-1111122-2022-1-100-2-211000000000000002-2-1111-1-1-1-11100-2020000110-1000
χ402222-122222-122-1-12-2-1-12-2-2-2-2-1-122-2-2-2-2-1-1-1-1200-2-20000-111111-1-1-111112-220221100-2-21100000000000000-22-1-111-1-111-1-10020-20000-1-101000
χ412-22-22222-2-2-22-22-2-202220000-222-200002-2-2-2-22i−2i2i−2i2i2i−2i−2i2000002-2-2000000000000002i−2i2i−2i2i−2i002i2i−2i−2i00002-200002i−2i000000000002-2000000000
χ422-22-22222-2-2-22-22-2-202220000-222-200002-2-2-2-22i−2i−2i2i2i2i−2i−2i2000002-2-200000000000000−2i2i−2i2i2i−2i002i2i−2i−2i0000-220000−2i2i00000000000-22000000000
χ432-22-22222-2-2-22-22-2-202220000-222-200002-2-2-2-2−2i2i2i−2i−2i−2i2i2i2000002-2-2000000000000002i−2i2i−2i−2i2i00−2i−2i2i2i0000-2200002i−2i00000000000-22000000000
χ442-22-22222-2-2-22-22-2-202220000-222-200002-2-2-2-2−2i2i−2i2i−2i−2i2i2i2000002-2-200000000000000−2i2i−2i2i−2i2i00−2i−2i2i2i00002-20000−2i2i000000000002-2000000000
χ452-22-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-21112i−2i2i−2i−i−iii-1000−i3i3-111−i3−i3i3i300003−3003−3−ii2i−2i2i−2i00−i−iii33−3−32-20000−ii3−3000000000-11−i3i30000000
χ462-22-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-21112i−2i−2i2i−i−iii-1000−i3i3-111−i3−i3i3i30000−33003−3i−i−2i2i2i−2i00−i−iii33−3−3-220000i−i−330000000001-1i3−i30000000
χ472-22-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-2111−2i2i2i−2iii−i−i-1000−i3i3-111−i3−i3i3i300003−300−33−ii2i−2i−2i2i00ii−i−i−3−333-220000−ii3−30000000001-1i3−i30000000
χ482-22-222-12-21-2-112-2-202-1-100−i3i3-2-1-11−i3−i3i3i32-2111−2i2i−2i2iii−i−i-1000−i3i3-111−i3−i3i3i30000−3300−33i−i−2i2i−2i2i00ii−i−i−3−3332-20000i−i−33000000000-11−i3i30000000
χ492-22-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-21112i−2i2i−2i−i−iii-1000i3−i3-111i3i3−i3−i30000−3300−33−ii2i−2i2i−2i00−i−iii−3−3332-20000−ii−33000000000-11i3−i30000000
χ502-22-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-21112i−2i−2i2i−i−iii-1000i3−i3-111i3i3−i3−i300003−300−33i−i−2i2i2i−2i00−i−iii−3−333-220000i−i3−30000000001-1−i3i30000000
χ512-22-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-2111−2i2i2i−2iii−i−i-1000i3−i3-111i3i3−i3−i30000−33003−3−ii2i−2i−2i2i00ii−i−i33−3−3-220000−ii−330000000001-1−i3i30000000
χ522-22-222-12-21-2-112-2-202-1-100i3−i3-2-1-11i3i3−i3−i32-2111−2i2i−2i2iii−i−i-1000i3−i3-111i3i3−i3−i300003−3003−3i−i−2i2i−2i2i00ii−i−i33−3−32-20000i−i3−3000000000-11i3−i30000000
χ5344444-2-2-2-2-24-2-244-24-2-21-2-2-2-2-2-2111111-2-2-2-214400-2-2-2-214-2-2-2-2111111100040000-2-20000-2-2-2-211111111000000000000000000000000000000
χ5444444-2-2-2-2-24-2-244-24-2-21-2-2-2-2-2-2111111-2-2-2-21-4-400222214-2-2-2-21111111000-400002200002222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5544444-2-2-2-2-24-2-244-2-4-2-212222-2-211-1-1-1-1-2-2-2-214400-2-2-2-21-42222111-1-1-1-1000-40000220000-2-2221111-1-1-1-1000000000000000000000000000000
χ5644444-2-2-2-2-24-2-244-2-4-2-212222-2-211-1-1-1-1-2-2-2-21-4-40022221-42222111-1-1-1-100040000-2-2000022-2-2-1-1-1-11111000000000000000000000000000000
χ574444-24-244-2-2-2-2-2-244-21-244-2-2-21-2-2-2-2-2-2-2-211-2004400001-2-2-21111111114000-2-20000-2-2-2-20000000000000000-20111100000000000000000000
χ584444-24-244-2-2-2-2-2-244-21-244-2-2-21-2-2-2-2-2-2-2-211-200-4-400001-2-2-2111111111-40002200002222000000000000000020-1-1-1-100000000000000000000
χ594444-24-244-2-2-2-2-2-24-4-21-2-4-422-21-2-22222-2-211-2004400001222-1-1111-1-1-1-1-4000220000-2-2-2-200000000000000002011-1-100000000000000000000
χ604444-24-244-2-2-2-2-2-24-4-21-2-4-422-21-2-22222-2-211-200-4-400001222-1-1111-1-1-1-14000-2-2000022220000000000000000-20-1-11100000000000000000000
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χ7144-4-44-2-22-2-2422-4-420-2-21000022-113-33-32-2-22-10000−2323−2323100000-11-13-33-30000000000000000−23233−33−33−33−3000000000000000000000000000000
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χ7444-4-4-244-444-2-4-422-40-2-24000022-4400002-2-22-400000000-2000002-220000000000000000000000000000000000000000000000000000023−2300000
χ7544-4-4-244-444-2-4-422-40-2-24000022-4400002-2-22-400000000-2000002-2200000000000000000000000000000000000000000000000000000−232300000
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χ774-44-44-24-22-4-44-44-420-24-2000024-220000-22-4-42−4i4i00−4i−4i4i4i-200000-2220000000000000000002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ784-44-44-2-2-222-4-224-420-2-2100−2i32i32-21-1i3i3−i3−i3-2222-14i−4i00−2i−2i2i2i1000−2i32i31-1-1i3i3−i3−i30000000023−230000−2i2i00ii−i−i−3−333000000000000000000000000000000
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χ804-44-44-2-2-222-4-224-420-2-21002i3−2i32-21-1−i3−i3i3i3-2222-14i−4i00−2i−2i2i2i10002i3−2i31-1-1−i3−i3i3i300000000−23230000−2i2i00ii−i−i33−3−3000000000000000000000000000000
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χ884-4-44444-4-4-4-4-44-444044400004-4-4-40000-4-4-44400000000400000-4-44000000000000000000000000000000000000000000000000000000000000
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χ994-4-44-2-2422-42-442-2-201-2-2−2i32i3001222−2i32i32i3−2i3-1-12-2-20000000010i3−i300-1-11i3−i3−i3i300000023−230000000000000000000000000000−333i−3i0000000000000000
χ1004-4-44-2-2422-42-442-2-201-2-2−2i32i3001222−2i32i32i3−2i3-1-12-2-20000000010i3−i300-1-11i3−i3−i3i3000000−232300000000000000000000000000003−3−3i3i0000000000000000
χ1014-4-44-2-2422-42-442-2-201-2-22i3−2i30012222i3−2i3−2i32i3-1-12-2-20000000010−i3i300-1-11−i3i3i3−i300000023−230000000000000000000000000000−33−3i3i0000000000000000
χ1024-4-44-2-2422-42-442-2-201-2-22i3−2i30012222i3−2i3−2i32i3-1-12-2-20000000010−i3i300-1-11−i3i3i3−i3000000−232300000000000000000000000000003−33i−3i0000000000000000
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χ1108-88-8-4-4-4-4444-44-444022200−4i34i3-222-22i32i3−2i3−2i32-2-2-2-200000000-10002i3−2i3-111−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-4444-44-4440222004i3−4i3-222-2−2i3−2i32i32i32-2-2-2-200000000-1000−2i32i3-111i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4-8-8444-44-480-42-40000-4-244000044-22-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444444-44-4-40222−4i34i3002-2-2-22i3−2i3−2i32i3-2-2-22200000000-102i3−2i30011-1−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444444-44-4-402224i3−4i3002-2-2-2−2i32i32i3−2i3-2-2-22200000000-10−2i32i30011-1i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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