Finite Group Databasebeta

← Group #13168453

Character table — Group #13168453

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121222446666121212121212121212121212441212121266666612121212121212121212222446666121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-111111111-1-111111111111-111-1-1-111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-111111-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-1111111-1-11111-111-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-11111-1-111-1-111-1-111-1-1-1-1-1-11111111-1-1-11111-1-1-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-1111-1-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-1-1-111111111-11-1-111-1-11111-1-1-1-1-11-11-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-111111111-1-1-1-1-1-11-1111111-1-1-1-11-11-1-111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1111-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-11-111-1111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-111-11-1-111-1-1111-111-1111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1111-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-111-1-1111111111111-11-1-1-1-1-1-111-1-11-11-1-111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-11111-1-11111111-111-1-111-1-1-1-11111-11-11-1-1-1-1-1111-11-1
χ17222222-1-12222-1-122-12-12-12-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-1022222002200-1-1-1-122000000000-100-1-12-1-1-100-1-1-1-10220000-1-100-1000
χ18222222-1-12222-1-122-12-12-12-12-1-12-1-1222200-1-1-1-12-122-1-1-1-1-1-1-1-10-2-22-2-2002200-1-1112200000000010011-2-1-1-10011-1-10-2-2000011001000
χ19222222-1-12222-1-122-12-12-12-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1022-22200-2-20011-1-1-2-2000000000-100-1-1211100-1-1110-2-2000011001000
χ20222222-1-12222-1-122-12-12-12-12-1-12-1-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-2-2-200-2-2001111-2-200000000010011-21110011110220000-1-100-1000
χ21222222-1-12222-1-122-12-1-2-12-12-1-12-1-1-2-22200-1-1-1-1-21-2-21111111102-2-222002200-1-111-2-2000000000-100-1-1-21-1-100111102-200001100-1000
χ22222222-1-12222-1-122-12-1-2-12-12-1-12-1-1-2-22200-1-1-1-1-21-2-2111111110-22-2-2-2002200-1-1-1-1-2-20000000001001121-1-100-1-1110-220000-1-1001000
χ23222222-1-12222-1-122-12-1-2-12-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-21111111102-222200-2-200111122000000000-100-1-1-2-1110011-1-10-220000-1-1001000
χ24222222-1-12222-1-122-12-1-2-12-12-1-12-1-1-2-2-2-200-1-1-1-1-21-2-2111111110-222-2-200-2-20011-1-122000000000100112-11100-1-1-1-102-200001100-1000
χ2522222-12222-1-122-12-1-122-1-12-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1200200-1-1-1-1-1-12200-1-12222-1-1-1-120-1-10002-1-1-1-100-1-120000-1-100000000
χ2622222-12222-1-122-12-1-122-1-12-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20020011-1-1112200-1-1-2-2-2-21111-20110002-1-11100-1-1-200001100000000
χ2722222-12222-1-122-12-1-122-1-12-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1200-200-1-111-1-1-2-2001122-2-2111120-1-1000-211-1-10011-200001100000000
χ2822222-12222-1-122-12-1-122-1-12-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-200-200111111-2-20011-2-222-1-1-1-1-2011000-21111001120000-1-100000000
χ2922222-12222-1-122-12-1-12-2-1-12-12-1-12-1112222-1-1-1-1-2-211-2-2111111-200-20011-1-1-1-12200112222-1-1-1-1-2011000-2-1-1-1-10011-200001100000000
χ3022222-12222-1-122-12-1-12-2-1-12-12-1-12-11122-2-2-1-1-1-1-2-211-2-2111111200-200-1-1-1-111220011-2-2-2-2111120-1-1000-2-1-111001120000-1-100000000
χ3122222-12222-1-122-12-1-12-2-1-12-12-1-12-111-2-222-1-1-1-1-2-211-2-2111111-2002001111-1-1-2-200-1-122-2-21111-2011000211-1-100-1-120000-1-100000000
χ3222222-12222-1-122-12-1-12-2-1-12-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-2111111200200-1-11111-2-200-1-1-2-222-1-1-1-120-1-10002111100-1-1-200001100000000
χ332222-1222-1-122222-12-1-122-1-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12220-1-1220022002200-1-1000000-12-1-1-1-1-1000-1-1-1-100000220000-1-10-100
χ342222-1222-1-122222-12-1-122-1-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12-2-201122002200-2-200-1-1000000-1-2-1-1111000-1-11100000-2-20000110100
χ352222-1222-1-122222-12-1-122-1-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2220-1-1-2-200-2-2002200110000001211-1-1-100011-1-100000-2-20000110100
χ362222-1222-1-122222-12-1-122-1-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-2011-2-200-2-200-2-200110000001-211111000111100000220000-1-10-100
χ372222-1222-1-122222-12-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-11-21111-2-21111-22-20-1-1-2-2002200-2-200-1-10000001211-1-11000-1-111000002-20000-1-10100
χ382222-1222-1-122222-12-1-1-22-1-1-1-12-1-12-2-20022-1-1-1-11-21111-2-21111-2-22011-2-20022002200-1-10000001-21111-1000-1-1-1-100000-220000110-100
χ392222-1222-1-122222-12-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-2111122-20-1-12200-2-200-2-20011000000-12-1-1-1-11000111100000-220000110-100
χ402222-1222-1-122222-12-1-1-22-1-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-211112-220112200-2-200220011000000-1-2-1-111-100011-1-1000002-20000-1-10100
χ4122-2-2222-2-222-2-22-2-22220-22-2-2-22-22-2002-22i−2i22-2-2000000000000000000002-22i−2i2-200002i−2i2i−2i2i2i−2i−2i000000002-22i−2i0000000000000000000
χ4222-2-2222-2-222-2-22-2-22220-22-2-2-22-22-2002-2−2i2i22-2-2000000000000000000002-2−2i2i2-20000−2i2i−2i2i−2i−2i2i2i000000002-2−2i2i0000000000000000000
χ4322-2-2222-2-222-2-22-2-22220-22-2-2-22-22-200-222i−2i22-2-200000000000000000000-222i−2i-2200002i−2i−2i2i−2i−2i2i2i00000000-222i−2i0000000000000000000
χ4422-2-2222-2-222-2-22-2-22220-22-2-2-22-22-200-22−2i2i22-2-200000000000000000000-22−2i2i-220000−2i2i2i−2i2i2i−2i−2i00000000-22−2i2i0000000000000000000
χ4522-2-22-12-2-22-11-221-2-1-1201-1-21-2-11213−32-22i−2i-1-111003−3003−333−3−3000000−i3i3-11−ii2-2003−32i−2i2i−2i−i−iii00−i3i30000-11−ii003−300000−i3i300000000
χ4622-2-22-12-2-22-11-221-2-1-1201-1-21-2-11213−32-2−2i2i-1-111003−3003−333−3−3000000i3−i3-11i−i2-2003−3−2i2i−2i2iii−i−i00i3−i30000-11i−i003−300000i3−i300000000
χ4722-2-22-12-2-22-11-221-2-1-1201-1-21-2-11213−3-222i−2i-1-111003−3003−333−3−3000000−i3i31-1−ii-2200−332i−2i−2i2iii−i−i00−i3i300001-1−ii00−3300000i3−i300000000
χ4822-2-22-12-2-22-11-221-2-1-1201-1-21-2-11213−3-22−2i2i-1-111003−3003−333−3−3000000i3−i31-1i−i-2200−33−2i2i2i−2i−i−iii00i3−i300001-1i−i00−3300000−i3i300000000
χ4922-2-22-12-2-22-11-221-2-1-1201-1-21-2-1121−332-22i−2i-1-11100−3300−33−3−333000000i3−i3-11−ii2-200−332i−2i2i−2i−i−iii00i3−i30000-11−ii00−3300000i3−i300000000
χ5022-2-22-12-2-22-11-221-2-1-1201-1-21-2-1121−332-2−2i2i-1-11100−3300−33−3−333000000−i3i3-11i−i2-200−33−2i2i−2i2iii−i−i00−i3i30000-11i−i00−3300000−i3i300000000
χ5122-2-22-12-2-22-11-221-2-1-1201-1-21-2-1121−33-222i−2i-1-11100−3300−33−3−333000000i3−i31-1−ii-22003−32i−2i−2i2iii−i−i00i3−i300001-1−ii003−300000−i3i300000000
χ5222-2-22-12-2-22-11-221-2-1-1201-1-21-2-1121−33-22−2i2i-1-11100−3300−33−3−333000000−i3i31-1i−i-22003−3−2i2i2i−2i−i−iii00−i3i300001-1i−i003−300000i3−i300000000
χ5344444-2-2-244-2-2-2-2-241-2-241-2-2-2-21-2-21-2-2440011114-2-2-2-2-211111100040000-2-200-2-200-2-2000000000000000-211000011000000000000000
χ5444444-2-2-244-2-2-2-2-241-2-241-2-2-2-21-2-21-2-2-4-40011114-2-2-2-2-2111111000-4000022002200220000000000000002-1-10000-1-1000000000000000
χ5544444-2-2-244-2-2-2-2-241-2-2-41-2-2-2-21-2-212244001111-422222-1-1-1-1-1-1000-40000-2-200-2-200220000000000000002110000-1-1000000000000000
χ5644444-2-2-244-2-2-2-2-241-2-2-41-2-2-2-21-2-2122-4-4001111-422222-1-1-1-1-1-10004000022002200-2-2000000000000000-2-1-1000011000000000000000
χ574444-24-2-2-2-244-2-24-2-2-214-2-21-21-2-21-24400001111-2-2-2-211-2-211110440-2-200000000-2-200000000000-20011-2000001100000000000000000
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χ594444-24-2-2-2-244-2-24-2-2-21-4-2-21-21-2-21-2-4-4000011112222-1-122-1-1-1-104-40-2-2000000002200000000000-20011200000-1-100000000000000000
χ604444-24-2-2-2-244-2-24-2-2-21-4-2-21-21-2-21-2-4-4000011112222-1-122-1-1-1-10-4402200000000-2-200000000000200-1-1-2000001100000000000000000
χ614444-2-244-2-2-2-244-2-2-21-24-21-21-2-21-2-2-2-200441111-2411-2-2-2-21111400000-2-200-2-2000000-2-2000000-2011000000110000000000000000000
χ624444-2-244-2-2-2-244-2-2-21-24-21-21-2-21-2-2-2-200-4-41111-2411-2-2-2-21111-4000002200220000002200000020-1-1000000-1-10000000000000000000
χ634444-2-244-2-2-2-244-2-2-21-2-4-21-21-2-21-2-222004411112-4-1-12222-1-1-1-1-4000002200-2-2000000-2-200000020-1-1000000110000000000000000000
χ644444-2-244-2-2-2-244-2-2-21-2-4-21-21-2-21-2-22200-4-411112-4-1-12222-1-1-1-1400000-2-2002200000022000000-2011000000-1-10000000000000000000
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χ914-4-44-24-2-222-4422-4-2-2-210-2212-12-2-120000001-11-100003i−3i003i−3i3i−3i0000−2i32i30000000023−2300000000000000i3−i3000000−3300000000000000000
χ924-4-44-24-2-222-4422-4-2-2-210-2212-12-2-120000001-11-100003i−3i003i−3i3i−3i00002i3−2i300000000−232300000000000000−i3i30000003−300000000000000000
χ934-4-44-24-2-222-4422-4-2-2-210-2212-12-2-120000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i300000000−232300000000000000i3−i30000003−300000000000000000
χ944-4-44-24-2-222-4422-4-2-2-210-2212-12-2-120000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i30000000023−2300000000000000−i3i3000000−3300000000000000000
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
χ9788-8-8-48-444-48-84-4-84-4-4204-4-24-2-442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-444-4-444-4442220-22-2-2-22-22-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-444-4-444-4442220-22-2-2-22-22-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-448-844-44-4-82-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-44-44-8-8-4484-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48-8-44448-8-44-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44-4444-44-442220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-4444-44-442220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4-4-8-84-444482-4-4024-444-2-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-488444-4-8-84-4-42-40-4-2-4-2442440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4444-4444-422202-22-2-2-22-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4444-4444-422202-22-2-2-22-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000

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