Finite Group Databasebeta

← Group #13169187

Character table — Group #13169187

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212444466661212121212121212121212124412121212661212121212121212121212121212222446666121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111111111111-1-111-1-1111111111-1-111111-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-111-1-111-1-1-1-1-1-111-111111-1-111-1-111-1-1-111-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-111111111-111-1-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1-1-1-111-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1111111-1-111111111-1-11-1-1-1-1-1-1-11111-11-11-1-1-111-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1111111111111-11-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1111-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-1-1111-111-111-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-11-111-111-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-111-1-1-1-1111111-1-11-1111111-1-1-1-111-1-11-11-1-1-1-1111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-111-11111111-1-1-1-1-11-11-1-1-111-1-1-111-1
χ17222222-1222-1-12-122-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1202200000022-1-1-1-1222200000000-1-12000-1-1-1-1-1-1-1-10220000-1-100-1000
χ18222222-1222-1-12-122-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2200000022-1-11122-2-200000000-11-2000-1-111-1-1110-2-2000011001000
χ19222222-1222-1-12-122-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1202-2000000-2-211-1-1-2-222000000001-1200011-1-111-1-10-2-2000011001000
χ20222222-1222-1-12-122-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-2000000-2-21111-2-2-2-20000000011-2000111111110220000-1-100-1000
χ21222222-1222-1-12-122-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-21111111120-2-2000000-2-2-1-1-1-122-2-2000000001120001111-1-1-1-102-20000-1-1001000
χ22222222-1222-1-12-122-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-202-2000000-2-2-1-1112222000000001-1-200011-1-1-1-1110-2200001100-1000
χ23222222-1222-1-12-122-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-21111111120-220000002211-1-1-2-2-2-200000000-112000-1-11111-1-10-2200001100-1000
χ24222222-1222-1-12-122-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111-2022000000221111-2-22200000000-1-1-2000-1-1-1-1111102-20000-1-1001000
χ2522222-122-1-12222-122-1-122-1-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1020222-1-1-1-1-1-12200-1-10022-1-1-1-1-1-12002-1-1-1-100-1-10020000-1-100000000
χ2622222-122-1-12222-122-1-122-1-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1020-222-1-1-1-111-2-2001100-2-21111-1-1-2002-1-111001100-200001100000000
χ2722222-122-1-12222-122-1-122-1-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-10-202-2-21111-1-12200-1-100-2-2111111200-211-1-100-1-100-200001100000000
χ2822222-122-1-12222-122-1-122-1-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-10-20-2-2-2111111-2-200110022-1-1-1-111-200-2111100110020000-1-100000000
χ2922222-122-1-12222-122-1-1-22-1-1-12-1-12-1112222-1-1-1-1-2-211-2-21111110-20-222-1-111112200-1-10022-1-1-1-1-1-1-200-2111100-1-100-200001100000000
χ3022222-122-1-12222-122-1-1-22-1-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-21111110-20222-1-111-1-1-2-2001100-2-21111-1-1200-211-1-100110020000-1-100000000
χ3122222-122-1-12222-122-1-1-22-1-1-12-1-12-111-2-222-1-1-1-1-2-211-2-2111111020-2-2-211-1-1112200-1-100-2-2111111-2002-1-11100-1-10020000-1-100000000
χ3222222-122-1-12222-122-1-1-22-1-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-21111110202-2-211-1-1-1-1-2-200110022-1-1-1-1112002-1-1-1-1001100-200001100000000
χ332222-122-12222-122-1-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12220-1-1222200002200-1-1000000-1-102-1-1-1-100-1-100-1-1000220000-1-10-100
χ342222-122-12222-122-1-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-22-20-1-122220000-2-20011000000-1-10-21-1-1-100110011000-2-20000110100
χ352222-122-12222-122-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-22011-2-2-2-200002200-1-10000001102-111100-1-100-1-1000-2-20000110100
χ362222-122-12222-122-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2011-2-2-2-20000-2-20011000000110-2111100110011000220000-1-10-100
χ372222-122-12222-122-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-211112-2-20-1-122-2-20000220011000000-1-10-2-1111001100-1-10002-20000110-100
χ382222-122-12222-122-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-21111-2-220-1-122-2-20000-2-200-1-1000000-1-102111100-1-10011000-220000-1-10100
χ392222-122-12222-122-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-2111122-2011-2-2220000220011000000110-2-1-1-1-1001100-1-1000-220000-1-10100
χ402222-122-12222-122-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-21111-222011-2-2220000-2-200-1-100000011021-1-1-100-1-100110002-20000110-100
χ412-2-2222222-22-2-2-2-2-222202-22-2-22-2-2-2002-22i−2i22-2-200000000000000002-22-200002i−2i002i−2i002i−2i2i2i−2i−2i2-200000000002i−2i00000000000000000
χ422-2-2222222-22-2-2-2-2-222202-22-2-22-2-2-2002-2−2i2i22-2-200000000000000002-22-20000−2i2i00−2i2i00−2i2i−2i−2i2i2i2-20000000000−2i2i00000000000000000
χ432-2-2222222-22-2-2-2-2-222202-22-2-22-2-2-200-222i−2i22-2-20000000000000000-22-2200002i−2i002i−2i00−2i2i−2i−2i2i2i-2200000000002i−2i00000000000000000
χ442-2-2222222-22-2-2-2-2-222202-22-2-22-2-2-200-22−2i2i22-2-20000000000000000-22-220000−2i2i00−2i2i002i−2i2i2i−2i−2i-220000000000−2i2i00000000000000000
χ452-2-222-122-112-2-2-21-22-1-1021-11-2-11-213−32-22i−2i-1-111003−3003−333−3−300002-2-113−3−i3i32i−2i00−ii002i−2i−i−iii-1100003−3−i3i300−ii0000000−i3i300000000
χ462-2-222-122-112-2-2-21-22-1-1021-11-2-11-213−32-2−2i2i-1-111003−3003−333−3−300002-2-113−3i3−i3−2i2i00i−i00−2i2iii−i−i-1100003−3i3−i300i−i0000000i3−i300000000
χ472-2-222-122-112-2-2-21-22-1-1021-11-2-11-213−3-222i−2i-1-111003−3003−333−3−30000-221-1−33−i3i32i−2i00−ii00−2i2iii−i−i1-10000−33−i3i300−ii0000000i3−i300000000
χ482-2-222-122-112-2-2-21-22-1-1021-11-2-11-213−3-22−2i2i-1-111003−3003−333−3−30000-221-1−33i3−i3−2i2i00i−i002i−2i−i−iii1-10000−33i3−i300i−i0000000−i3i300000000
χ492-2-222-122-112-2-2-21-22-1-1021-11-2-11-21−332-22i−2i-1-11100−3300−33−3−33300002-2-11−33i3−i32i−2i00−ii002i−2i−i−iii-110000−33i3−i300−ii0000000i3−i300000000
χ502-2-222-122-112-2-2-21-22-1-1021-11-2-11-21−332-2−2i2i-1-11100−3300−33−3−33300002-2-11−33−i3i3−2i2i00i−i00−2i2iii−i−i-110000−33−i3i300i−i0000000−i3i300000000
χ512-2-222-122-112-2-2-21-22-1-1021-11-2-11-21−33-222i−2i-1-11100−3300−33−3−3330000-221-13−3i3−i32i−2i00−ii00−2i2iii−i−i1-100003−3i3−i300−ii0000000−i3i300000000
χ522-2-222-122-112-2-2-21-22-1-1021-11-2-11-21−33-22−2i2i-1-11100−3300−33−3−3330000-221-13−3−i3i3−2i2i00i−i002i−2i−i−iii1-100003−3−i3i300i−i0000000i3−i300000000
χ5344444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-2-21-2-2004411114-2-2-2-2-21111110004000000-2-2-2-200-2-20000000000-20000011001100000000000000000
χ5444444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-2-21-2-200-4-411114-2-2-2-2-2111111000-4000000222200220000000000200000-1-100-1-100000000000000000
χ5544444-2-24-2-2-2-24-2-24-21-2-4-21-2-2-21-2-212200441111-422222-1-1-1-1-1-1000-400000022-2-200-2-20000000000200000-1-1001100000000000000000
χ5644444-2-24-2-2-2-24-2-24-21-2-4-21-2-2-21-2-212200-4-41111-422222-1-1-1-1-1-10004000000-2-22200220000000000-2000001100-1-100000000000000000
χ574444-24-2-244-2-2-2-24-21-2-241-2-2-21-2-21-24400001111-2-2-2-211-2-2111140400000000000-2-200-2-2000000000-2-200000110011000000000000000
χ584444-24-2-244-2-2-2-24-21-2-241-2-2-21-2-21-24400001111-2-2-2-211-2-21111-40-4000000000002200220000000002200000-1-100-1-1000000000000000
χ594444-24-2-244-2-2-2-24-21-2-2-41-2-2-21-2-21-2-4-4000011112222-1-122-1-1-1-140-400000000000-2-200220000000002-200000-1-10011000000000000000
χ604444-24-2-244-2-2-2-24-21-2-2-41-2-2-21-2-21-2-4-4000011112222-1-122-1-1-1-1-404000000000002200-2-2000000000-22000001100-1-1000000000000000
χ614444-2-24-2-2-244-24-2-2-2-214-2-211-2-21-2-2-2-244001111-2411-2-2-2-211110400-2-2-2-2-2-2000000000000000011000-21100000000000000000000000
χ624444-2-24-2-2-244-24-2-2-2-214-2-211-2-21-2-2-2-2-4-4001111-2411-2-2-2-211110-4002222220000000000000000-1-10002-1-100000000000000000000000
χ634444-2-24-2-2-244-24-2-2-2-21-4-2-211-2-21-2-222440011112-4-1-12222-1-1-1-10-400-2-2-2-2220000000000000000110002-1-100000000000000000000000
χ644444-2-24-2-2-244-24-2-2-2-21-4-2-211-2-21-2-222-4-40011112-4-1-12222-1-1-1-104002222-2-20000000000000000-1-1000-21100000000000000000000000
χ6544-4-4444-4-4-4-4-4444-44440-4-4-44-4-4-4440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-4-24-22-442-222-4-21-2-20-1-22212-2-120000001-11-10000−3i3i00−3i3i−3i3i0000000000000023−23002i3−2i30000000000000000−i3i300−33000000000000000
χ824-44-4-24-22-442-222-4-21-2-20-1-22212-2-120000001-11-10000−3i3i00−3i3i−3i3i00000000000000−232300−2i32i30000000000000000i3−i3003−3000000000000000
χ834-4-4444-244-4-22-42-4-4-2-240-224-42-2-42200004i−4i-2-222000000000000000000000000−2i2i004i−4i00000000000000000000−2i2i00000000000000000
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χ854-4-444-2-24-22-22-422-4-21-20-2-1-222122-123−23004i−4i11-1-10023−2300−33−3−3330000000000−2i32i3−2i2i00−2i2i0000000000000000i3−i300i−i00000000000000000
χ864-4-444-2-24-22-22-422-4-21-20-2-1-222122-123−2300−4i4i11-1-10023−2300−33−3−33300000000002i3−2i32i−2i002i−2i0000000000000000−i3i300−ii00000000000000000
χ874-4-444-2-24-22-22-422-4-21-20-2-1-222122-1−2323004i−4i11-1-100−2323003−333−3−300000000002i3−2i3−2i2i00−2i2i0000000000000000−i3i300i−i00000000000000000
χ884-4-444-2-24-22-22-422-4-21-20-2-1-222122-1−232300−4i4i11-1-100−2323003−333−3−30000000000−2i32i32i−2i002i−2i0000000000000000i3−i300−ii00000000000000000
χ894-4-44-244-24-44-42-4-42-24-20-2-4-222422-4004-400-2-2220000000000000000-224-4000000000000000000-2200000000000000000000000000000
χ904-4-44-244-24-44-42-4-42-24-20-2-4-222422-400-4400-2-22200000000000000002-2-440000000000000000002-200000000000000000000000000000
χ914-4-44-2-24-2-224-42-422-2-210-221-12-2-12223−234-40011-1-100−330023−23−3−3330000-22-2223−2300000000000000001-10000−3300000000000000000000000
χ924-4-44-2-24-2-224-42-422-2-210-221-12-2-12223−23-440011-1-100−330023−23−3−33300002-22-2−23230000000000000000-1100003−300000000000000000000000
χ934-4-44-2-24-2-224-42-422-2-210-221-12-2-122−23234-40011-1-1003−300−232333−3−30000-22-22−232300000000000000001-100003−300000000000000000000000
χ944-4-44-2-24-2-224-42-422-2-210-221-12-2-122−2323-440011-1-1003−300−232333−3−300002-22-223−230000000000000000-110000−3300000000000000000000000
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
χ9788-8-88-4-4-844448-4-4-8-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-44-8-844-4-4842-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-48444-8-8-48-44-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-444444-4-4-442220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444444-4-4-442220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4-84-44-4-8448-42-404244-4-2-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4844-4-884-84-4-4-4204-4-2-2-442440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444-44-4444-42220-22-2-22-22-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444-44-4444-42220-22-2-22-22-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-4-48-8-4444-842-4-4024-44-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4-44-44444422202-22-2-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4-44-44444422202-22-2-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000

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