Finite Group Databasebeta

← Group #13169188

Character table — Group #13169188

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212124444121212121212121212121212121212122266661212121212121212121212121212121222444661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-111111111111-1-111111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-11111-1-11111-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-111-1-11111-1-111-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-111-1-1-1-1-111-1-1-1-111-1-1-1-11-1-111-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-11111111111-11-1-1-1-1-1-1111111-1-11-11-1-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-11-1-1-1-1-1-1-1111111-11-11-111-1-1-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-11-1-111-1-111-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-111-11111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-111-11111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-11111-1-111-1-1-1-1-1-11-11-111-1-1-1-1-1-111111-1-111-1-111-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-111111111-11111111-1-1-1-1-1-1-11-11-111-1-1-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-1-1-111-1-1-1-11111111-1111111-1-1-1-1-1-1111-11-1-1-1-1-1-1111-11-1
χ17222222-122-1-122-1222-1-122-1-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12022222200-1-100-1-12200000000-1-120-1-100-1-1-1-100-1-122000-1-10000-1000
χ18222222-122-1-122-1222-1-122-1-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-120-2-2-2-22200-1-100112200000000-11-20-1-10011-1-10011-2-20001100001000
χ19222222-122-1-122-1222-1-122-1-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-202222-2-2001100-1-1-2-2000000001-1201100-1-11100-1-1-2-20001100001000
χ20222222-122-1-122-1222-1-122-1-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-2-2-2-2-200110011-2-20000000011-2011001111001122000-1-10000-1000
χ21222222-122-1-122-1222-1-1-22-1-12-1-12-1-1-2-22200-1-1-1-1-21-2-211111111-202-222-2-200-1-1001122000000001-1-201100-1-1-1-100112-2000110000-1000
χ22222222-122-1-122-1222-1-1-22-1-12-1-12-1-1-2-22200-1-1-1-1-21-2-211111111-20-22-2-2-2-200-1-100-1-122000000001120110011-1-100-1-1-22000-1-100001000
χ23222222-122-1-122-1222-1-1-22-1-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-211111111202-2222200110011-2-200000000-1-1-20-1-100-1-1110011-22000-1-100001000
χ24222222-122-1-122-1222-1-1-22-1-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-21111111120-22-2-222001100-1-1-2-200000000-1120-1-100111100-1-12-2000110000-1000
χ2522222-12-1222-122-12-12-12-12-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1220000-1-1-1-1222200-1-1-1-122-1-1-1-12002-1-1-1-100-1-1-1-1000000200-1-1000000
χ2622222-12-1222-122-12-12-12-12-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-12-20000-1-11122-2-200-1-111-2-21111200-2-1-11100-1-111000000-20011000000
χ2722222-12-1222-122-12-12-12-12-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-22000011-1-1-2-2220011-1-1-2-21111-200211-1-10011-1-1000000-20011000000
χ2822222-12-1222-122-12-12-12-12-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-200001111-2-2-2-200111122-1-1-1-1-200-21111001111000000200-1-1000000
χ2922222-12-1222-122-12-12-1-2-12-1-12-1-12-1112222-1-1-1-1-2-211-2-2111111-2-200001111222200-1-1-1-122-1-1-1-1-200-2111100-1-1-1-1000000-20011000000
χ3022222-12-1222-122-12-12-1-2-12-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-2111111-22000011-1-122-2-200-1-111-2-21111-200211-1-100-1-111000000200-1-1000000
χ3122222-12-1222-122-12-12-1-2-12-1-12-1-12-111-2-222-1-1-1-1-2-211-2-21111112-20000-1-111-2-2220011-1-1-2-21111200-2-1-1110011-1-1000000200-1-1000000
χ3222222-12-1222-122-12-12-1-2-12-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-2111111220000-1-1-1-1-2-2-2-200111122-1-1-1-12002-1-1-1-1001111000000-20011000000
χ332222-1222-1222-122-1-1-122-1-12-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-10222-1-1002200-1-122002200000002-1-100-1-1-1-100-1-1-1-1002200000-1-10-100
χ342222-1222-1222-122-1-1-122-1-12-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-102-2-211002200-1-1-2-200220000000-21-100-1-11100-1-11100-2-200000110100
χ352222-1222-1222-122-1-1-122-1-12-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-222-1-100-2-200112200-2-200000002-110011-1-10011-1-100-2-200000110100
χ362222-1222-1222-122-1-1-122-1-12-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-21100-2-20011-2-200-2-20000000-211001111001111002200000-1-10-100
χ372222-1222-1222-122-1-1-12-2-1-12-1-12-1-12-2-20022-1-1-1-11-21111-2-211110-22-2-1-100-2-200-1-1-2-2002200000002110011-1-100-1-111002-200000-1-10100
χ382222-1222-1222-122-1-1-12-2-1-12-1-12-1-12-2-20022-1-1-1-11-21111-2-211110-2-221100-2-200-1-12200220000000-2-1100111100-1-1-1-100-2200000110-100
χ392222-1222-1222-122-1-1-12-2-1-12-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-21111022-2-1-100220011-2-200-2-2000000021-100-1-1-1-100111100-2200000110-100
χ402222-1222-1222-122-1-1-12-2-1-12-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-2111102-2211002200112200-2-20000000-2-1-100-1-1110011-1-1002-200000-1-10100
χ4122-2-2222-2-22-22-2-2-222220-22-22-22-2-2-2002i−2i2i−2i22-2-200000000000000000000002i−2i2i−2i002i−2i2i−2i2-222-2-200000000002i−2i2i−2i00000000000000000
χ4222-2-2222-2-22-22-2-2-222220-22-22-22-2-2-2002i−2i−2i2i22-2-200000000000000000000002i−2i−2i2i002i−2i−2i2i-22-2-22200000000002i−2i−2i2i00000000000000000
χ4322-2-2222-2-22-22-2-2-222220-22-22-22-2-2-200−2i2i2i−2i22-2-20000000000000000000000−2i2i2i−2i00−2i2i2i−2i-22-2-2220000000000−2i2i2i−2i00000000000000000
χ4422-2-2222-2-22-22-2-2-222220-22-22-22-2-2-200−2i2i−2i2i22-2-20000000000000000000000−2i2i−2i2i00−2i2i−2i2i2-222-2-20000000000−2i2i−2i2i00000000000000000
χ4522-2-22-121-22-2-1-2-212-12-10121-1-2-11-213−32i−2i2i−2i-1-111003−3003−333−3−3000000−i3i3−i3i32i−2i2i−2i00−ii−ii2-2-1-1110000−i3i3−i3i300−ii−ii0000000003−3000000
χ4622-2-22-121-22-2-1-2-212-12-10121-1-2-11-213−32i−2i−2i2i-1-111003−3003−333−3−3000000−i3i3i3−i32i−2i−2i2i00−iii−i-2211-1-10000−i3i3i3−i300−iii−i000000000−33000000
χ4722-2-22-121-22-2-1-2-212-12-10121-1-2-11-213−3−2i2i2i−2i-1-111003−3003−333−3−3000000i3−i3−i3i3−2i2i2i−2i00i−i−ii-2211-1-10000i3−i3−i3i300i−i−ii000000000−33000000
χ4822-2-22-121-22-2-1-2-212-12-10121-1-2-11-213−3−2i2i−2i2i-1-111003−3003−333−3−3000000i3−i3i3−i3−2i2i−2i2i00i−ii−i2-2-1-1110000i3−i3i3−i300i−ii−i0000000003−3000000
χ4922-2-22-121-22-2-1-2-212-12-10121-1-2-11-21−332i−2i2i−2i-1-11100−3300−33−3−333000000i3−i3i3−i32i−2i2i−2i00−ii−ii2-2-1-1110000i3−i3i3−i300−ii−ii000000000−33000000
χ5022-2-22-121-22-2-1-2-212-12-10121-1-2-11-21−332i−2i−2i2i-1-11100−3300−33−3−333000000i3−i3−i3i32i−2i−2i2i00−iii−i-2211-1-10000i3−i3−i3i300−iii−i0000000003−3000000
χ5122-2-22-121-22-2-1-2-212-12-10121-1-2-11-21−33−2i2i2i−2i-1-11100−3300−33−3−333000000−i3i3i3−i3−2i2i2i−2i00i−i−ii-2211-1-10000−i3i3i3−i300i−i−ii0000000003−3000000
χ5222-2-22-121-22-2-1-2-212-12-10121-1-2-11-21−33−2i2i−2i2i-1-11100−3300−33−3−333000000−i3i3−i3i3−2i2i−2i2i00i−ii−i2-2-1-1110000−i3i3−i3i300i−ii−i000000000−33000000
χ5344444-2-2-24-2-2-24-2-24-2-214-2-21-2-21-2-21-2-2440011114-2-2-2-2-2111111400000-2-200-2-20000-2-200000000-2000110000110000000000000000000
χ5444444-2-2-24-2-2-24-2-24-2-214-2-21-2-21-2-21-2-2-4-40011114-2-2-2-2-2111111-400000220022000022000000002000-1-10000-1-10000000000000000000
χ5544444-2-2-24-2-2-24-2-24-2-21-4-2-21-2-21-2-212244001111-422222-1-1-1-1-1-1-4000002200-2-20000-2-2000000002000-1-10000110000000000000000000
χ5644444-2-2-24-2-2-24-2-24-2-21-4-2-21-2-21-2-2122-4-4001111-422222-1-1-1-1-1-1400000-2-2002200002200000000-2000110000-1-10000000000000000000
χ574444-24-24-2-2-24-2-24-2-21-24-21-2-21-2-21-24400001111-2-2-2-211-2-211110044-2-200000000-2-200000000000-2-20000011000011000000000000000
χ584444-24-24-2-2-24-2-24-2-21-24-21-2-21-2-21-24400001111-2-2-2-211-2-2111100-4-4220000000022000000000002200000-1-10000-1-1000000000000000
χ594444-24-24-2-2-24-2-24-2-21-2-4-21-2-21-2-21-2-4-4000011112222-1-122-1-1-1-1004-4-2-2000000002200000000000-2200000110000-1-1000000000000000
χ604444-24-24-2-2-24-2-24-2-21-2-4-21-2-21-2-21-2-4-4000011112222-1-122-1-1-1-100-442200000000-2-2000000000002-200000-1-1000011000000000000000
χ614444-2-24-2-244-2-24-2-21-2-241-2-21-2-21-2-2-2-200441111-2411-2-2-2-2111104000000-2-200-2-20000-2-2000000000-2001100001100000000000000000
χ624444-2-24-2-244-2-24-2-21-2-241-2-21-2-21-2-2-2-200-4-41111-2411-2-2-2-211110-4000000220022000022000000000200-1-10000-1-100000000000000000
χ634444-2-24-2-244-2-24-2-21-2-2-41-2-21-2-21-2-222004411112-4-1-12222-1-1-1-10-40000002200-2-20000-2-2000000000200-1-100001100000000000000000
χ644444-2-24-2-244-2-24-2-21-2-2-41-2-21-2-21-2-22200-4-411112-4-1-12222-1-1-1-104000000-2-20022000022000000000-200110000-1-100000000000000000
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χ6844-4-44-2-22-4-22-2-4224-2-2102-2-1-22122-123−23−4i4i0011-1-10023−2300−33−3−3330000002i3−2i3002i−2i00002i−2i000000000000−i3i30000−ii0000000000000000000
χ6944-4-44-2-22-4-22-2-4224-2-2102-2-1-22122-1−23234i−4i0011-1-100−2323003−333−3−30000002i3−2i300−2i2i0000−2i2i000000000000−i3i30000i−i0000000000000000000
χ7044-4-44-2-22-4-22-2-4224-2-2102-2-1-22122-1−2323−4i4i0011-1-100−2323003−333−3−3000000−2i32i3002i−2i00002i−2i000000000000i3−i30000−ii0000000000000000000
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χ7444-4-4-2-24224-4-22-42-21-2-20-1-2212-2-12223−2300−4i4i11-1-100−330023−23−3−333000000002i3−2i3002i−2i00002i−2i000000000000−i3i30000−ii00000000000000000
χ7544-4-4-2-24224-4-22-42-21-2-20-1-2212-2-122−2323004i−4i11-1-1003−300−232333−3−3000000002i3−2i300−2i2i0000−2i2i000000000000−i3i30000i−i00000000000000000
χ7644-4-4-2-24224-4-22-42-21-2-20-1-2212-2-122−232300−4i4i11-1-1003−300−232333−3−300000000−2i32i3002i−2i00002i−2i000000000000i3−i30000−ii00000000000000000
χ774-44-444444-44-4-4-4-4-444404-44-44-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-44-24-24-442-4-42-4-24-20-2-4-22422-42000000-22-2200000000000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000000
χ824-44-4-2444-2-44-42-4-42-2-240-2242-2-422-4000000-22-220000000000000000−2i32i30000000000000000000000000000−2i32i3000000000000000000000
χ834-44-4-2444-2-44-42-4-42-2-240-2242-2-422-4000000-22-2200000000000000002i3−2i300000000000000000000000000002i3−2i3000000000000000000000
χ844-44-4-24-24-22-2-422-42-21-20-2-1-22122-120000001-11-100003i−3i003i−3i3i−3i0000−2i32i30000000023−23000000000000000000i3−i30000−33000000000000000
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χ864-44-4-24-24-22-2-422-42-21-20-2-1-22122-120000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i300000000−2323000000000000000000i3−i300003−3000000000000000
χ874-44-4-24-24-22-2-422-42-21-20-2-1-22122-120000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i30000000023−23000000000000000000−i3i30000−33000000000000000
χ884-4-44444-4-4-4-4-4444-44440-4-4-4-4-4-44440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-422-44-24-44-2-20-422-4224-2-2000000-222-200000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ904-4-4444-2-4-422-44-24-44-2-20-422-4224-2-2000000-222-2000000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ914-4-444-242-4-4-4244-2-4-24-202-422-42-24-2000000-222-20000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ924-4-444-242-4-4-4244-2-4-24-202-422-42-24-2000000-222-200000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ934-4-44-244-42-4-4-4-2442-2-24022-422-4-2-24000000-222-200000000000000000000000000000000000000000000000000000000000000023−230000
χ944-4-44-244-42-4-4-4-2442-2-24022-422-4-2-24000000-222-2000000000000000000000000000000000000000000000000000000000000000−23230000
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
χ9788-8-8-48-4-84-44844-8-4-42-40424-4-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-444-44-4444-42220-22-22-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-444-44-4444-42220-22-22-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-484-44-844-8-4-420-4424-4-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48-4-4-8844-8442-4-4024-4-2-44-2440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-4-44-44444422202-22-22-2-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4-44-44444422202-22-22-2-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-44-84448-4-4-8-4-42044-244-2-4-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-8444-8-4-484-42-404-244-24-42-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-8-84-48-442-4-40-244-2442-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-4-442220-2-2-2-2-2-2222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-4-442220-2-2-2-2-2-2222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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