Finite Group Databasebeta

← Group #13168429

Character table — Group #13168429

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121222446666121212121212121212121212441212121266666612121212121212121212244446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-111111111-1-111111111111-111-1-11-11111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1-1111111-1-11111-111-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-111-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111111-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-1-1-111-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-11-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-111111111-11-1-111-1-11111-1-1-1-1-11-11-1-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-11111111-1-1-1-11-11-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-11111111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11-111-1-1-1111-1-111-1-11-111-111-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1111-1-1-111-1-1111-111-111-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-111-1-11111111111111-1-1-1-1-1-1-111-1-11-11-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-11111-1-11111111-111-1-111-1-1-1-11111-11-11-1-1-1-1-1111-1-11
χ17222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1200200-1-1-1-122-1-100-1-12222-1-1-1-120-1-10020-1-1-1-100-1-120000-1-100000000
χ18222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-20020011-1-1-2-21100-1-122-2-21111-20110020-1-11100-1-1-200001100000000
χ19222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1200-200-1-11122-1-10011-2-2-2-2111120-1-100-2011-1-10011-200001100000000
χ20222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-200-2001111-2-2110011-2-222-1-1-1-1-201100-201111001120000-1-100000000
χ21222222-1222-1-12-122-12-1-2-12-12-1-12-1-1112222-1-1-1-1-2-2-2-211111111-200-20011-1-122-1-100112222-1-1-1-1-201100-20-1-1-1-10011-200001100000000
χ22222222-1222-1-12-122-12-1-2-12-12-1-12-1-11122-2-2-1-1-1-1-2-2-2-211111111200-200-1-1-1-1-2-211001122-2-2111120-1-100-20-1-111001120000-1-100000000
χ23222222-1222-1-12-122-12-1-2-12-12-1-12-1-111-2-222-1-1-1-1-2-2-2-211111111-200200111122-1-100-1-1-2-2-2-21111-2011002011-1-100-1-120000-1-100000000
χ24222222-1222-1-12-122-12-1-2-12-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111200200-1-111-2-21100-1-1-2-222-1-1-1-120-1-10020111100-1-1-200001100000000
χ2522222-122-1-12222-122-1-122-1-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12220222200-1-122-1-10000000000-1-1-1-1-1-10200-1-1-1-1000002200-1-100-1000
χ2622222-122-1-12222-122-1-122-1-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12-2-20-2-22200-1-122110000000000-11-1-1110-200-1-11100000-2-20011001000
χ2722222-122-1-12222-122-1-122-1-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-222022-2-20011-2-2-1-100000000001-111-1-1020011-1-100000-2-20011001000
χ2822222-122-1-12222-122-1-122-1-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-20-2-2-2-20011-2-21100000000001111110-2001111000002200-1-100-1000
χ2922222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-1-211111-2-21111-22-2022-2-200-1-1221100000000001-111-1-10-200-1-111000002-2001100-1000
χ3022222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-1-211111-2-21111-2-220-2-2-2-200-1-122-1-100000000001111110200-1-1-1-100000-2200-1-1001000
χ3122222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-2111122-2022220011-2-2110000000000-1-1-1-1-1-10-200111100000-2200-1-1001000
χ3222222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-211112-220-2-2220011-2-2-1-10000000000-11-1-111020011-1-1000002-2001100-1000
χ332222-122-12222-122-1-1-122-1-12-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-10222-1-1002200002222-1-10000000200-1-1-1-1-1-100-1-1-1-1022000000-1-10-100
χ342222-122-12222-122-1-1-122-1-12-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-10-2-221100220000-2-222-1-10000000-20011-11-1-10011-1-10-2-2000000110100
χ352222-122-12222-122-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1022-2-1-100-2-2000022-2-2110000000200-1-11-11100-1-1110-2-2000000110100
χ362222-122-12222-122-1-1-122-1-12-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-21100-2-20000-2-2-2-2110000000-200111111001111022000000-1-10-100
χ372222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-211111102-2-2-1-100220000-2-2-2-2-1-10000000200-1-111-1-100111102-2000000-1-10100
χ382222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-22200-1-1-1-11-211-2-21111110-22-2110022000022-2-2-1-10000000-200111-1-1-100-1-1110-22000000110-100
χ392222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-211111102-22-1-100-2-20000-2-222110000000200-1-1-11110011-1-10-22000000110-100
χ402222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-200-1-1-1-11-211-2-21111110-2221100-2-200002222110000000-20011-1-11100-1-1-1-102-2000000-1-10100
χ4122-2-2222-22-22-2-2-2-222220-2-22-2-222-2-2002-22i−2i22-2-2000000000000000000002-22i−2i2i−2i00002-22i−2i2i2i−2i−2i000000002-22i−2i0000000000000000000
χ4222-2-2222-22-22-2-2-2-222220-2-22-2-222-2-2002-2−2i2i22-2-2000000000000000000002-2−2i2i−2i2i00002-2−2i2i−2i−2i2i2i000000002-2−2i2i0000000000000000000
χ4322-2-2222-22-22-2-2-2-222220-2-22-2-222-2-200-222i−2i22-2-200000000000000000000-222i−2i2i−2i0000-22−2i2i−2i−2i2i2i00000000-222i−2i0000000000000000000
χ4422-2-2222-22-22-2-2-2-222220-2-22-2-222-2-200-22−2i2i22-2-200000000000000000000-22−2i2i−2i2i0000-222i−2i2i2i−2i−2i00000000-22−2i2i0000000000000000000
χ4522-2-222-1-22-2-11-21-22-12-101-2-1-21-12113−32-22i−2i-1-11100003−33−333−3−3000000−i3i3-112i−2i−ii003−32-22i−2i−i−iii00−i3i30000-11−ii003−300000−i3i300000000
χ4622-2-222-1-22-2-11-21-22-12-101-2-1-21-12113−32-2−2i2i-1-11100003−33−333−3−3000000i3−i3-11−2i2ii−i003−32-2−2i2iii−i−i00i3−i30000-11i−i003−300000i3−i300000000
χ4722-2-222-1-22-2-11-21-22-12-101-2-1-21-12113−3-222i−2i-1-11100003−33−333−3−3000000−i3i31-12i−2i−ii00−33-22−2i2iii−i−i00−i3i300001-1−ii00−3300000i3−i300000000
χ4822-2-222-1-22-2-11-21-22-12-101-2-1-21-12113−3-22−2i2i-1-11100003−33−333−3−3000000i3−i31-1−2i2ii−i00−33-222i−2i−i−iii00i3−i300001-1i−i00−3300000−i3i300000000
χ4922-2-222-1-22-2-11-21-22-12-101-2-1-21-1211−332-22i−2i-1-1110000−33−33−3−333000000i3−i3-112i−2i−ii00−332-22i−2i−i−iii00i3−i30000-11−ii00−3300000i3−i300000000
χ5022-2-222-1-22-2-11-21-22-12-101-2-1-21-1211−332-2−2i2i-1-1110000−33−33−3−333000000−i3i3-11−2i2ii−i00−332-2−2i2iii−i−i00−i3i30000-11i−i00−3300000−i3i300000000
χ5122-2-222-1-22-2-11-21-22-12-101-2-1-21-1211−33-222i−2i-1-1110000−33−33−3−333000000i3−i31-12i−2i−ii003−3-22−2i2iii−i−i00i3−i300001-1−ii003−300000−i3i300000000
χ5222-2-222-1-22-2-11-21-22-12-101-2-1-21-1211−33-22−2i2i-1-1110000−33−33−3−333000000−i3i31-1−2i2ii−i003−3-222i−2i−i−iii00−i3i300001-1i−i003−300000i3−i300000000
χ5344444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2004411114-2-2-211-2-21111400000-2-200-2-2-2-2000000000000-2011000000110000000000000000000
χ5444444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-200-4-411114-2-2-211-2-21111-4000002200222200000000000020-1-1000000-1-10000000000000000000
χ5544444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-22200441111-4222-1-122-1-1-1-1-4000002200-2-2-2-200000000000020-1-1000000110000000000000000000
χ5644444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-22200-4-41111-4222-1-122-1-1-1-1400000-2-2002222000000000000-2011000000-1-10000000000000000000
χ574444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-244001111-24-2-2-2-211111100040000-2-2000000-2-2-2-2000000000000-2011000011000000000000000
χ584444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-2-4-4001111-24-2-2-2-2111111000-4000022000000222200000000000020-1-10000-1-1000000000000000
χ594444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122440011112-42222-1-1-1-1-1-1000-40000-2-200000022-2-200000000000020110000-1-1000000000000000
χ604444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122-4-40011112-42222-1-1-1-1-1-10004000022000000-2-222000000000000-20-1-1000011000000000000000
χ614444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-211110440-2-200000000-2-200000000000-200110-200001100000000000000000
χ624444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-211110-4-4022000000002200000000000200-1-1020000-1-100000000000000000
χ634444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-104-40-2-2000000002200000000000-20011020000-1-100000000000000000
χ644444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-10-4402200000000-2-200000000000200-1-10-200001100000000000000000
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χ924-4-444-24-422-4-444-2-44-2-20-422-2-2-4224000000-222-200000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ934-4-44-2442-4-4-4-4-2442-2-24022-4-2422-4-2000000-222-200000000000000000000000000000000000000000000000000000000000000023−230000
χ944-4-44-2442-4-4-4-4-2442-2-24022-4-2422-4-2000000-222-2000000000000000000000000000000000000000000000000000000000000000−23230000
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
χ9788-8-8-4-484-448-84-84-4-42-404-2-4-24-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-44-44444-42220-2-22-2-222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-44-44444-42220-2-22-2-222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
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
χ1048-8-888-4-4-844448-4-4-8-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-8-844-4-4842-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48444-8-8-48-44-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-4-442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-4-442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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