Finite Group Databasebeta

← Group #13168352

Character table — Group #13168352

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212124444121212121212121212121212121212121212121212122212121212121212121212121244444661212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-11111111111111-1-1-11111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111-111111-1-1-1-1-1-111111111111111-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1111-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11111-11-1-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-111-1-11111-1-1-1-111-1-11-111-1-111-1-11-11-1-111-1-111-11-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-111-1-1-11111-1-1-1-11-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-11-1-1-11111-1-1-111-11-1-111-1-111-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-11111-11-1-1-11111-1-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-11111-1-1-1-11-111-1-111-1-111-11-1-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-1-11111-1-1-11-1111-1-1-1-111-111-11-1-111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1111111-1-1-1-11111111-11-1-1-11111-1-1-1-1-11111-1-1-1-11-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-111-1-111-1-1-1-111111111-11-1-111-1-1111-11-1-111-1-111-11-1-11
χ17222222-1222-1-1-12222-1-122-12-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-1-1-10022-1-1-1-1-1-1-1-1222000-1-1-1-1000002000-1-1-1-10000000
χ18222222-1222-1-1-12222-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-220022-2-21111-1-10022-1-1-1-1-1-1-1-1-2-2-2000111100000-200011110000000
χ19222222-1222-1-1-12222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-12-200-2-222-1-1-1-11100-2-211111111-2-22000-1-1-1-100000-200011110000000
χ20222222-1222-1-1-12222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-211111100-2-21111111122-20001111000002000-1-1-1-10000000
χ21222222-1222-1-1-12222-1-1-22-12-1-1-1-1-12-2-21111112222-1-1-1-1-1-1-1-1-2-2-2111111-2-200222211-1-11100-2-2-1-1-1-1111122-2000-1-11100000-2000-1-1110000000
χ22222222-1222-1-1-12222-1-1-22-12-1-1-1-1-12-2-211111122-2-2-1-1-1-1-1-1-1-1-2-2-21111112-20022-2-2-1-1111100-2-2-1-1-1-11111-2-2200011-1-100000200011-1-10000000
χ23222222-1222-1-1-12222-1-1-22-12-1-1-1-1-12-2-2111111-2-2221111-1-1-1-1-2-2-2111111-2200-2-22211-1-1-1-100221111-1-1-1-1-2-2-2000-1-11100000200011-1-10000000
χ24222222-1222-1-1-12222-1-1-22-12-1-1-1-1-12-2-2111111-2-2-2-21111-1-1-1-1-2-2-21111112200-2-2-2-2-1-111-1-100221111-1-1-1-122200011-1-100000-2000-1-1110000000
χ2522222-1222-1222-1-12-12-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1202200-1-1222200-1-1000000000000-1-122-1-1-1-1-1-1-1-1200020000-1-1-10000
χ2622222-1222-1222-1-12-12-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-120-2-200-1-122220011000000000000-11-2-2-1-1-1-11111-2000-200001110000
χ2722222-1222-1222-1-12-12-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20220011-2-2-2-200-1-10000000000001-1221111-1-1-1-1-2000-200001110000
χ2822222-1222-1222-1-12-12-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-20011-2-2-2-2001100000000000011-2-211111111200020000-1-1-10000
χ2922222-1222-1222-1-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-202-200-1-1-2-22200-1-1000000000000112-2-1-111-1-1112000-20000-1-110000
χ3022222-1222-1222-1-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-20-2200-1-1-2-22200110000000000001-1-22-1-11111-1-1-20002000011-10000
χ3122222-1222-1222-1-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111202-2001122-2-200-1-1000000000000-112-211-1-1-1-111-20002000011-10000
χ3222222-1222-1222-1-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111120-22001122-2-20011000000000000-1-1-2211-1-111-1-12000-20000-1-110000
χ332222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-10222-1-10000002222-1-1-1-1-1-1-1-1-1-10002-1-10000-1-1-1-1002200000000-1-100
χ342222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-122002222-1-1-1-12-1-122-1-1-1-102-2-2-1-100000022-2-2-1-1-1-1-1-1-1-1-1-1000-2110000111100-2-2000000001100
χ352222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-10-22211000000-2-22211111111110002-1-10000-1-1-1-100-2-2000000001100
χ362222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-211000000-2-2-2-21111111111000-21100001111002200000000-1-100
χ372222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-2111122002222-1-1-1-1-211-2-211110-22-2-1-1000000-2-22211-1-1-1-11111000-2-110000-1-111002-200000000-1100
χ382222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-2111122002222-1-1-1-1-211-2-211110-2-22-1-1000000-2-2-2-211-1-1-1-1111100021-1000011-1-100-22000000001-100
χ392222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-21111022-2110000002222-1-11111-1-1-1-1000-2-110000-1-11100-22000000001-100
χ402222-122-1-1222222-1-1-12-2-12-1-1-1-122-111-2-21111-2-200-2-2-2-2-1-1-1-1-211-2-2111102-221100000022-2-2-1-11111-1-1-1-100021-1000011-1-1002-200000000-1100
χ4122-2-2222-222-22-2-2-2-222202-2-2-22-22-2-2000000002-22-222-2-222-2-200000000000002-22-2002-200000022-2-200002-200002-2000000000002-2000000000
χ4222-2-2222-222-22-2-2-2-222202-2-2-22-22-2-2000000002-2-2222-2-222-2-200000000000002-2-2200-2200000022-2-20000-220000-2200000000000-22000000000
χ4322-2-2222-222-22-2-2-2-222202-2-2-22-22-2-200000000-222-2-2-22222-2-20000000000000-222-2002-2000000-2-2220000-2200002-200000000000-22000000000
χ4422-2-2222-222-22-2-2-2-222202-2-2-22-22-2-200000000-22-22-2-22222-2-20000000000000-22-2200-22000000-2-22200002-20000-22000000000002-2000000000
χ4522-2-222-1-2221-11-2-2-22-1-1021-21-11-11-2003−333−3−32-22-2-1-111-1-1110003−333−3−300002-22-23−3-113−30000-1-11133−3−32-20000-113−3000000000-113−30000000
χ4622-2-222-1-2221-11-2-2-22-1-1021-21-11-11-2003−333−3−32-2-22-1-111-1-1110003−333−3−300002-2-22−331-13−30000-1-11133−3−3-2200001-1−330000000001-1−330000000
χ4722-2-222-1-2221-11-2-2-22-1-1021-21-11-11-2003−333−3−3-222-211-1-1-1-1110003−333−3−30000-222-23−3-11−33000011-1-1−3−333-220000-113−30000000001-1−330000000
χ4822-2-222-1-2221-11-2-2-22-1-1021-21-11-11-2003−333−3−3-22-2211-1-1-1-1110003−333−3−30000-22-22−331-1−33000011-1-1−3−3332-200001-1−33000000000-113−30000000
χ4922-2-222-1-2221-11-2-2-22-1-1021-21-11-11-200−33−3−3332-22-2-1-111-1-111000−33−3−33300002-22-2−33-11−330000-1-111−3−3332-20000-11−33000000000-11−330000000
χ5022-2-222-1-2221-11-2-2-22-1-1021-21-11-11-200−33−3−3332-2-22-1-111-1-111000−33−3−33300002-2-223−31-1−330000-1-111−3−333-2200001-13−30000000001-13−30000000
χ5122-2-222-1-2221-11-2-2-22-1-1021-21-11-11-200−33−3−333-222-211-1-1-1-111000−33−3−3330000-222-2−33-113−3000011-1-133−3−3-220000-11−330000000001-13−30000000
χ5222-2-222-1-2221-11-2-2-22-1-1021-21-11-11-200−33−3−333-22-2211-1-1-1-111000−33−3−3330000-22-223−31-13−3000011-1-133−3−32-200001-13−3000000000-11−330000000
χ5344444-2-244-2-2-2-2-2-24-2-214-21-2-2-2-211-244-2-2-2-2-2-2004400001111-2-2-2111111400000-2-2-2-2-2-20000000000000000-2000111100000000000000000000
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χ584444-24-2-2-24-2-2-244-2-21-24-2-2-2111-2-2-2-2-2-2-21111-4-400222211114-2-2-2-211110-40022000000220022-1-1-1-1-1-1-1-1000000000000000000000000000000
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χ864-44-4-24-2-22-4-2224-42-21-2022-21-1-12-222i3−2i300−i3i3−i3i3000023−2323−231-1-1102i3−2i300−i3i3−i3i3000000000000000000−33−33−3i3i−3i3i000000000000000000000000000000
χ874-44-4-24-2-22-4-2224-42-21-2022-21-1-12-222i3−2i300−i3i3−i3i30000−2323−23231-1-1102i3−2i300−i3i3−i3i30000000000000000003−33−33i−3i3i−3i000000000000000000000000000000
χ884-44-4-2-24-2224-4-4-2221-2-20-121-2222-2-1−2i32i300−2i32i3−2i32i3000000001-1-110i3−i300i3−i3i3−i30000000000000023−2300000000000000000000−333i−3i0000000000000000
χ894-44-4-2-24-2224-4-4-2221-2-20-121-2222-2-1−2i32i300−2i32i3−2i32i3000000001-1-110i3−i300i3−i3i3−i300000000000000−2323000000000000000000003−3−3i3i0000000000000000
χ904-44-4-2-24-2224-4-4-2221-2-20-121-2222-2-12i3−2i3002i3−2i32i3−2i3000000001-1-110−i3i300−i3i3−i3i30000000000000023−2300000000000000000000−33−3i3i0000000000000000
χ914-44-4-2-24-2224-4-4-2221-2-20-121-2222-2-12i3−2i3002i3−2i32i3−2i3000000001-1-110−i3i300−i3i3−i3i300000000000000−2323000000000000000000003−33i−3i0000000000000000
χ924-4-44444-4-4-4-4-44-4444440-44-4-4-44-4-4400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ934-4-4444-2-4-4-422-2-4444-2-20-4-2-422-222400000000000023−23−2323-22-2200000000000000000000000000023−23−23230000000000000000000000000000000000
χ944-4-4444-2-4-4-422-2-4444-2-20-4-2-422-2224000000000000−232323−23-22-22000000000000000000000000000−232323−230000000000000000000000000000000000
χ954-4-444-24-4-42-4-442-24-24-202-22-4-4422-20000000000000000-22-22000000000000000000000000000000000000000000000000000000000023−2300000
χ964-4-444-24-4-42-4-442-24-24-202-22-4-4422-20000000000000000-22-220000000000000000000000000000000000000000000000000000000000−232300000
χ974-4-44-24422-4-4-44-44-2-2-24024222-2-4-4-20000000000000000-22-220000000000000000000000000−2i32i30000−2i32i32i3−2i3000000000000000000000000000000
χ984-4-44-24422-4-4-44-44-2-2-24024222-2-4-4-20000000000000000-22-2200000000000000000000000002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000
χ994-4-44-24-222-422-2-44-2-21-202-22-1-1122-200003i−3i−3i3i000023−23−23231-11-1000003i−3i−3i3i00000000000000002i3−2i3−333−3−i3i3i3−i3000000000000000000000000000000
χ1004-4-44-24-222-422-2-44-2-21-202-22-1-1122-200003i−3i−3i3i0000−232323−231-11-1000003i−3i−3i3i0000000000000000−2i32i33−3−33i3−i3−i3i3000000000000000000000000000000
χ1014-4-44-24-222-422-2-44-2-21-202-22-1-1122-20000−3i3i3i−3i000023−23−23231-11-100000−3i3i3i−3i0000000000000000−2i32i3−333−3i3−i3−i3i3000000000000000000000000000000
χ1024-4-44-24-222-422-2-44-2-21-202-22-1-1122-20000−3i3i3i−3i0000−232323−231-11-100000−3i3i3i−3i00000000000000002i3−2i33−3−33−i3i3i3−i3000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-484-4-4-88-84442-4-4024-24-44-44-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-44-4444422202-2-2-22-22-2-20043−43−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4-44-4444422202-2-2-22-22-2-200−43432323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-48-84-444-44-8-4-4204-2-4-444-22400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-444-444-4442220-2-222-2-2-22-2−4i34i3002i3−2i32i3−2i300000000-111-102i3−2i300−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-444-444-4442220-2-222-2-2-22-24i3−4i300−2i32i3−2i32i300000000-111-10−2i32i300i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-8-8444-44-48-4-42042444-4-2-2-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48444-8-884-4-42-4-40-2-4-244-444200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444444-44-4-42220-22-2-2-22-2-2200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444444-44-4-42220-22-2-2-22-2-220000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

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