Finite Group Databasebeta

← Group #13168186

Character table — Group #13168186

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212224436661212121212121212121212122444666666121212121212121212124412121212666661212121212121212121212244446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11-1-11111111111-1-111111111-111-1-111-11111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1111-1-111-1-1-111-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-111-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111-111-1-1111111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-111-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-111-1-1-1-1-1-1-1-1-1-111-1-11111111-1-111-1-11-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-111-1-11111111111111-1-1-1-1-1-1-1-1-111-11-11-1-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1111111111111-111-1-1-1-11-1-1-1-11111-1-11-11-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-111-1-1111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-11-111-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1111-1-111-1-1-1-1111-111-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1111111-1-1111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11111-1-1-1-1-1-11111111-1-11111-11111-1-1-1-1-1-11-11-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1111111111-1-1-11-11-1-1-1-1-1111-1-11
χ17222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-102020022-1-1-1-1-1-1-1-1002222-1-1-1-10-1-100220-1-1-1-100-1-120000-1-100000000
χ18222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2020022-1-1-1-1111100-2-2-2-211110-1-1002-20-1-1110011-200001100000000
χ19222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1020-200-2-21111-1-1-1-10022-2-2111101100-22011-1-100-1-1-200001100000000
χ20222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-20-200-2-21111111100-2-222-1-1-1-101100-2-201111001120000-1-100000000
χ21222222-1222-1-12-122-12-1-2-12-12-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-20-20022-1-11111-1-1002222-1-1-1-10-1-100-2-20111100-1-1-200001100000000
χ22222222-1222-1-12-122-12-1-2-12-12-1-12-1-11122-2-2-1-1-1-1-2-2-2-211111111020-20022-1-111-1-11100-2-2-2-211110-1-100-22011-1-1001120000-1-100000000
χ23222222-1222-1-12-122-12-1-2-12-12-1-12-1-111-2-222-1-1-1-1-2-2-2-2111111110-20200-2-211-1-111-1-10022-2-21111011002-20-1-11100-1-120000-1-100000000
χ24222222-1222-1-12-122-12-1-2-12-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111020200-2-211-1-1-1-11100-2-222-1-1-1-101100220-1-1-1-10011-200001100000000
χ2522222-122-1-12222-122-1-122-1-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1202222-1-122220000-1-100000000-1-1-1-1-1-102-1-100-1-1000220000-1-100-1000
χ2622222-122-1-12222-122-1-122-1-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-22-2-2-1-12222000011000000001-1-111-10-2-1-10011000-2-2000011001000
χ2722222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1202-22211-2-2-2-20000-1-100000000-111-1-11021100-1-1000-2-2000011001000
χ2822222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-2-211-2-2-2-2000011000000001111110-2110011000220000-1-100-1000
χ2922222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-22200-1-1-1-11-21111-2-2111120-2-222-1-122-2-200001100000000-1-1-1-1-110-21100110002-200001100-1000
χ3022222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-22200-1-1-1-11-21111-2-21111-202-2-2-2-1-122-2-20000-1-1000000001-1-1111021100-1-1000-220000-1-1001000
χ3122222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-2111120-222211-2-22200001100000000-111-1-1-10-2-1-10011000-220000-1-1001000
χ3222222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-21111-2022-2-211-2-2220000-1-10000000011111-102-1-100-1-10002-200001100-1000
χ332222-122-12222-122-1-1-122-1-12-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-12220-1-1000000222222-1-1000000200-1-10-1-100-1-1-1-1-1-1000220000-1-10-100
χ342222-122-12222-122-1-1-122-1-12-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1-22-20110000002222-2-2-1-1000000-200110-1100-1-111-1-1000-2-20000110100
χ352222-122-12222-122-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-12-220-1-1000000-2-2-2-22211000000200-1-101-10011-1-111000-2-20000110100
χ362222-122-12222-122-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2011000000-2-2-2-2-2-211000000-2001101100111111000220000-1-10-100
χ372222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-1-2111-2-21111112-2-20-1-1000000-2-222-2-2-1-1000000200-1-1011001111-1-10002-20000-1-10100
χ382222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-1-2111-2-2111111-2-22011000000-2-22222-1-1000000-2001101-10011-1-1-1-1000-220000110-100
χ392222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-211111122-20-1-100000022-2-2-2-211000000200-1-10-1100-1-11111000-220000110-100
χ402222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-2111111-22201100000022-2-22211000000-200110-1-100-1-1-1-1110002-20000-1-10100
χ4122-2-2222-2-2-22-22-22-22220-2-22-2-222-2-2002-22i−2i22-2-20000000000000000002-22-200002i−2i002i−2i2i−2i2i2i−2i−2i02-2000000000002i−2i000000000000000
χ4222-2-2222-2-2-22-22-22-22220-2-22-2-222-2-2002-2−2i2i22-2-20000000000000000002-22-20000−2i2i00−2i2i−2i2i−2i−2i2i2i02-200000000000−2i2i000000000000000
χ4322-2-2222-2-2-22-22-22-22220-2-22-2-222-2-200-222i−2i22-2-2000000000000000000-22-2200002i−2i002i−2i−2i2i−2i−2i2i2i0-22000000000002i−2i000000000000000
χ4422-2-2222-2-2-22-22-22-22220-2-22-2-222-2-200-22−2i2i22-2-2000000000000000000-22-220000−2i2i00−2i2i2i−2i2i2i−2i−2i0-2200000000000−2i2i000000000000000
χ4522-2-222-1-2-2-2-11212-2-12-101-2-1-21-12113−32-22i−2i-1-11100003−33−333−3−30000002-2-113−3−i3i3−ii002i−2i2i−2i−i−iii0-11000003−3−i3i300−ii00000−i3i300000000
χ4622-2-222-1-2-2-2-11212-2-12-101-2-1-21-12113−32-2−2i2i-1-11100003−33−333−3−30000002-2-113−3i3−i3i−i00−2i2i−2i2iii−i−i0-11000003−3i3−i300i−i00000i3−i300000000
χ4722-2-222-1-2-2-2-11212-2-12-101-2-1-21-12113−3-222i−2i-1-11100003−33−333−3−3000000-221-1−33−i3i3−ii002i−2i−2i2iii−i−i01-100000−33−i3i300−ii00000i3−i300000000
χ4822-2-222-1-2-2-2-11212-2-12-101-2-1-21-12113−3-22−2i2i-1-11100003−33−333−3−3000000-221-1−33i3−i3i−i00−2i2i2i−2i−i−iii01-100000−33i3−i300i−i00000−i3i300000000
χ4922-2-222-1-2-2-2-11212-2-12-101-2-1-21-1211−332-22i−2i-1-1110000−33−33−3−3330000002-2-11−33i3−i3−ii002i−2i2i−2i−i−iii0-1100000−33i3−i300−ii00000i3−i300000000
χ5022-2-222-1-2-2-2-11212-2-12-101-2-1-21-1211−332-2−2i2i-1-1110000−33−33−3−3330000002-2-11−33−i3i3i−i00−2i2i−2i2iii−i−i0-1100000−33−i3i300i−i00000−i3i300000000
χ5122-2-222-1-2-2-2-11212-2-12-101-2-1-21-1211−33-222i−2i-1-1110000−33−33−3−333000000-221-13−3i3−i3−ii002i−2i−2i2iii−i−i01-1000003−3i3−i300−ii00000−i3i300000000
χ5222-2-222-1-2-2-2-11212-2-12-101-2-1-21-1211−33-22−2i2i-1-1110000−33−33−3−333000000-221-13−3−i3i3i−i00−2i2i2i−2i−i−iii01-1000003−3−i3i300i−i00000i3−i300000000
χ5344444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-244001111-24-2-211-2-21111000400-2-2-2-2-2-20000000000000001100-20011000000000000000000000
χ5444444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2-4-4001111-24-2-211-2-21111000-400222222000000000000000-1-100200-1-1000000000000000000000
χ5544444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-222440011112-422-1-122-1-1-1-1000-400-2-2-2-2220000000000000001100200-1-1000000000000000000000
χ5644444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-222-4-40011112-422-1-122-1-1-1-10004002222-2-2000000000000000-1-100-20011000000000000000000000
χ574444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-2004411114-2-2-2-2-2111111040000000000-2-2-2-200-2-2000000000000-2000110011000000000000000
χ584444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-200-4-411114-2-2-2-2-21111110-40000000000222200220000000000002000-1-100-1-1000000000000000
χ594444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-212200441111-422222-1-1-1-1-1-10-4000000000022-2-200-2-20000000000002000-1-10011000000000000000
χ604444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-212200-4-41111-422222-1-1-1-1-1-1040000000000-2-2220022000000000000-20001100-1-1000000000000000
χ614444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-211114040-2-20000000000-2-200000000-2001100-200001100000000000000000
χ624444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-21111-40-402200000000002200000000200-1-10020000-1-100000000000000000
χ634444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-140-40-2-200000000002200000000-200110020000-1-100000000000000000
χ644444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-1-4040220000000000-2-200000000200-1-100-200001100000000000000000
χ6544-4-44-24-4224-44-4-2-44-2-20-42-2224-22-4004-400-2-222000000000000000000-224-400000000000000000-220000000000000000000000000000
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χ7144-4-4-2442-4-44-4-2-442-2-2402242-4-2-2-4200004i−4i-2-222000000000000000000000000004i−4i00−2i2i00000000000000000000−2i2i000000000000000
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χ834-44-4-244-2-44-442-4-42-2-240-2-2-42-42242000000-22-2200000000000000002i3−2i3000000000000000000000002i3−2i300000000000000000000000000
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χ854-44-4-2-24-22-2-442-422-21-20-212-122-1-220000001-11-1003i−3i00003i−3i3i−3i00002i3−2i30000000000−232300000000000−i3i300000003−300000000000000000
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χ884-4-44444-44-4-4-4-44-444440-4-4-444-4-4-440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
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χ924-4-444-24-4-22-4-4-44244-2-20-422-2-2-4224000000-222-20000000000000000000000000000000000000000000000000000000000000−2323000000
χ934-4-44-24424-4-4-424-4-2-2-24022-4-2422-4-2000000-222-2000000000000000000000000000000000000000000000000000000000000000−2i32i30000
χ944-4-44-24424-4-4-424-4-2-2-24022-4-2422-4-2000000-222-20000000000000000000000000000000000000000000000000000000000000002i3−2i30000
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
χ9788-8-8-4-484448-8-4-8-44-42-404-2-4-24-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4444-44-44-442220-2-22-2-222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4444-44-44-442220-2-22-2-222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-484-44-4-844-8-4-420-4-4-24-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4-4-884-444-842-4-402-4444-24-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-44-44-44444222022-2-2-2-2-22-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-44-44-44444222022-2-2-2-2-22-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4-8-4444-8-448-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-448-8444-4-8-42-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-44-8-8484-4-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-44444-44-42220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-44444-44-42220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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