Finite Group Databasebeta

← Group #13170731

Character table — Group #13170731

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666333466666666612122222443666121212121212121212121212222244466666666121212121212121244446666666612121212121212121212121222412121212121244664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111111111-1111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-1111-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11-11111-1-111111-1-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-1-111-1-1-1-1-1-1-11-1-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111-1-111-1-111-1-1111111-1-111-1-1-1-1-1-111-1111-1-1111111-11-1-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-11-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-11-1-1-1-11111-1-1-1111111-1-1-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-111-1-1111-1111-1-111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-11111-1-111-1-1-1-1-1-1111-1-1-111-1-111-1-11-1111-1-111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-11111-1-1-1-111-1111111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-11
χ17222222-1-12222-1-1222-1-122-1-12-1-1-1-12-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-122222202222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-12200-1-1-1-10000002-1-1000000000
χ18222222-1-12222-1-1222-1-122-1-12-1-1-1-12-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22-2022-2-2-1-111-1-111000000001111-1-1112-200-1-111000000-211000000000
χ19222222-1-12222-1-1222-1-122-1-12-1-1-1-12-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-220-2-22211-1-111-1-100000000111111-1-1-220011-1-1000000-211000000000
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χ21222222-1-12222-1-1222-1-1-22-1-12-1-1-1-1211222200-1-1-1-1-2-2-2-2111111112222-2-202222-1-1-1-1111100000000-1-1-1-1-1-1-1-1-2-2001111000000-211000000000
χ22222222-1-12222-1-1222-1-1-22-1-12-1-1-1-121122-2-200-1-1-1-1-2-2-2-211111111-2-2-2-2-22022-2-2-1-11111-1-1000000001111-1-111-220011-1-10000002-1-1000000000
χ23222222-1-12222-1-1222-1-1-22-1-12-1-1-1-1211-2-22200-1-1-1-1-2-2-2-211111111-2-2-2-22-20-2-22211-1-1-1-11100000000111111-1-12-200-1-1110000002-1-1000000000
χ24222222-1-12222-1-1222-1-1-22-1-12-1-1-1-1211-2-2-2-200-1-1-1-1-2-2-2-2111111112222220-2-2-2-21111-1-1-1-100000000-1-1-1-111112200-1-1-1-1000000-211000000000
χ2522222-1222-12-1222-1-12-12-12-1-12-12-1-122002222-1-1-1-12-1-1-122-1-1-1-1-1-1000002200-1-10022002222-1-10022000000-1-10-12-100-1-1-1-1-1-10200000-1-1000-10
χ2622222-1222-12-1222-1-12-12-12-1-12-12-1-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1000002-200-1-100220022-2-21100-2-2000000-1-10-1-2100-1-111110-2000001100010
χ2722222-1222-12-1222-1-12-12-12-1-12-12-1-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-100000-22001100-2-200-2-222-1-100-2-200000011012-10011-1-1-1-10-2000001100010
χ2822222-1222-12-1222-1-12-12-12-1-12-12-1-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100000-2-2001100-2-200-2-2-2-21100220000001101-21001111110200000-1-1000-10
χ2922222-1222-12-1222-1-12-1-2-12-1-12-12-1-1-2-2002222-1-1-1-1-2111-2-211111100000-2-200-1-1002200-2-222-1-10022000000-1-101-210011-1-1110-200000-1-100010
χ3022222-1222-12-1222-1-12-1-2-12-1-12-12-1-1-2-20022-2-2-1-1-1-1-2111-2-211111100000-2200-1-1002200-2-2-2-21100-2-2000000-1-1012-1001111-1-1020000011000-10
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χ3222222-1222-12-1222-1-12-1-2-12-1-12-12-1-1-2-200-2-2-2-2-1-1-1-1-2111-2-21111110000022001100-2-20022-2-2110022000000110-12-100-1-111-1-10-200000-1-100010
χ332222-1222-12-1222-12-1-122-1-12-1-12-12-122220022-1-1-1-1-12-1-1-1-122-1-1-1-10000202-1-10022002200-1-12222000000-1-100-10-12-1-100-1-1-1-120000-1-10000-100
χ342222-1222-12-1222-12-1-122-1-12-1-12-12-1222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1000020-2-1-1002200220011-2-2-2-2000000-1-100-101-2-1-1001111-20000110000100
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χ362222-1222-12-1222-12-1-122-1-12-1-12-12-122-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10000-20-21100-2-200-2-20011-2-2220000001100101-21100111120000-1-10000-100
χ372222-1222-12-1222-12-1-12-2-1-12-1-12-12-1-2-2220022-1-1-1-11-21111-2-211110000-20-2-1-1002200-2-200-1-12222000000-1-100101-21100-1-111-20000-1-10000100
χ382222-1222-12-1222-12-1-12-2-1-12-1-12-12-1-2-22200-2-2-1-1-1-11-21111-2-211110000-202-1-1002200-2-20011-2-2-2-2000000-1-10010-12110011-1-120000110000-100
χ392222-1222-12-1222-12-1-12-2-1-12-1-12-12-1-2-2-2-20022-1-1-1-11-21111-2-21111000020-21100-2-2002200-1-122-2-20000001100-101-2-1-100-1-11120000110000-100
χ402222-1222-12-1222-12-1-12-2-1-12-1-12-12-1-2-2-2-200-2-2-1-1-1-11-21111-2-2111100002021100-2-200220011-2-2220000001100-10-12-1-10011-1-1-20000-1-10000100
χ4122-2-2222-2-2-2222-2-2-222202-2-2-2-2-222-20000000022-2-200000000000022-2-200000000000000000002i−2i2i−2i22-2-20000000000000000000002i−2i2i−2i00000
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χ462-22-2222-222-2-2-22-2-22220-2-2-2222-2-2-20000002i−2i2-2-22000000000000-22-220000000000000002i−2i2i−2i0000-22-220000000000002i−2i00000000000−2i2i000
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χ522-2-222222-2-2-2-2-2-2222220-222-2-2-2-2-2200-22-22002-22-20000000000002-2-22000-22-22-22-220000000000002-2-22-22-2200000000000000000000000000
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χ914-4-444-2-2-2-42-42224-2-2-2102-2122-12-1-223−23004-4001-11-1000023−23−33−3−333000000000-2200-220023−23000000000000001-1000000−33000000000000000000
χ924-4-444-2-2-2-42-42224-2-2-2102-2122-12-1-223−2300-44001-11-1000023−23−33−3−3330000000002-2002-200−232300000000000000-110000003−3000000000000000000
χ934-4-444-2-2-2-42-42224-2-2-2102-2122-12-1-2−2323004-4001-11-10000−23233−333−3−3000000000-2200-2200−2323000000000000001-10000003−3000000000000000000
χ944-4-444-2-2-2-42-42224-2-2-2102-2122-12-1-2−232300-44001-11-10000−23233−333−3−30000000002-2002-20023−2300000000000000-11000000−33000000000000000000
χ954-4-44-24442-42-4-4-4-24-2-2402-2422-42-4-2004-40000-22-220000000000000000000-22004-4000000000000000000-220000000000000000000000000000
χ964-4-44-24442-42-4-4-4-24-2-2402-2422-42-4-200-440000-22-2200000000000000000002-200-440000000000000000002-20000000000000000000000000000
χ974-4-44-24-2-22-42-422-24-21-2021-22-12-12-223−234-400001-11-10000−3323−23−3−3330000000-2200-220023−23000000000000001-1000000−3300000000000000000000
χ984-4-44-24-2-22-42-422-24-21-2021-22-12-12-223−23-4400001-11-10000−3323−23−3−33300000002-2002-200−232300000000000000-110000003−300000000000000000000
χ994-4-44-24-2-22-42-422-24-21-2021-22-12-12-2−23234-400001-11-100003−3−232333−3−30000000-2200-2200−2323000000000000001-10000003−300000000000000000000
χ1004-4-44-24-2-22-42-422-24-21-2021-22-12-12-2−2323-4400001-11-100003−3−232333−3−300000002-2002-20023−2300000000000000-11000000−3300000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-44-848-4-44-84-4-420-44-244-2-4240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-444-8-48-444-8-42-40-4-244-242-440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-844-4-48-8442-4-40244-244-4-4-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4444-4-4-444422202-2-2-2-2-222-200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4444-4-4-444422202-2-2-2-2-222-200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-448-4-844-4-84-4-42044-2-4-424-24000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-44-484-84-44-8-42-404-24-42-4-244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4-4444-4442220-2-2-2222-2-2-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-4-4444-4442220-2-2-2222-2-2-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4884444-8-8-4-42-4-40-2-4-4-244442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-4444444-4-42220-222-2-2-2-2-2243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-4444444-4-42220-222-2-2-2-2-22−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000

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