Finite Group Databasebeta

← Group #13168347

Character table — Group #13168347

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212124444121212121212121212121212121212121212121212122212121212121212121212121244444661212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-111111111111-1-1-11111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-1-1-1111111111111-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-1111111111111111111-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-11-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-11-1-11-1-111-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-111111-1-1-1-111-1-111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1111111-1-1-1-111-1-11-111-1-111-1-1-111-1-11111-1-1-11-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-111-11-1111-1-1-1-111-1-1-11111-1-1-1-11-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-11-1-1-11111-1-11-11-11-1-1-1-11111-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-11111-11-1-1-11111-1-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11-111-1-111-1-111-11-1-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1-1-11111-1-1-11-1111-1-1-1-1111-11-11-1-1-1-11111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-11111-1-1-1-11111111-11-1-1-11111-1-1-1-1-11111-1-1-1-11-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-111-1-111-1-111-1-1-1-1-1-111111111-11-1-111-1-111-111-1-11111-1-1-11-1-11
χ17222222-1222-1-12-1222-1-1222-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-12200222222-1-1-1-1-1-100-1-1-1-1-1-1-1-1222000-1-1-1-1000020000-1-100-1-100000
χ18222222-1222-1-12-1222-1-1222-1-1-1-1-1-12-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-12-2002222-2-21111-1-100-1-1-1-1-1-1-1-1-2-2-200011110000-2000011001100000
χ19222222-1222-1-12-1222-1-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-2221111-1-1-1-12-1-122-1-1-1-1-2200-2-2-2-222-1-1-1-1110011111111-2-22000-1-1-1-10000-2000011001100000
χ20222222-1222-1-12-1222-1-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-2-2111111001111111122-20001111000020000-1-100-1-100000
χ21222222-1222-1-12-1222-1-1-222-1-1-1-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-211-2-21111-2-20022-2-22211-1-11100-1-1-1-1111122-2000-1-1110000-20000-1-1001100000
χ22222222-1222-1-12-1222-1-1-222-1-1-1-1-1-1211-2-2111122-2-2-1-1-1-1-1-1-1-1-211-2-21111-220022-2-2-2-2-1-1111100-1-1-1-11111-2-2200011-1-10000200001100-1-100000
χ23222222-1222-1-12-1222-1-1-222-1-1-1-1-1-1211-2-21111-2-2221111-1-1-1-1-211-2-211112-200-2-2222211-1-1-1-1001111-1-1-1-1-2-2-2000-1-1110000200001100-1-100000
χ24222222-1222-1-12-1222-1-1-222-1-1-1-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-211-2-211112200-2-222-2-2-1-111-1-1001111-1-1-1-122200011-1-10000-20000-1-1001100000
χ2522222-1222-122-12-12-12-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-102220000-1-1222200-1-10000000000-1-122-1-1-1-1-1-1-1-10200200-1-100-10000
χ2622222-1222-122-12-12-12-12-1-1-1222-1-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-102-2-20000-1-1222200110000000000-11-2-2-1-1-1-111110-200-200110010000
χ2722222-1222-122-12-12-12-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-222000011-2-2-2-200-1-100000000001-1221111-1-1-1-10-200-200110010000
χ2822222-1222-122-12-12-12-12-1-1-1222-1-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2000011-2-2-2-20011000000000011-2-2111111110200200-1-100-10000
χ2922222-1222-122-12-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-22-20000-1-1-2-22200-1-10000000000112-2-1-111-1-1110200-200-1-10010000
χ3022222-1222-122-12-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-2-220000-1-1-2-222001100000000001-1-22-1-11111-1-10-2002001100-10000
χ3122222-1222-122-12-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111022-200001122-2-200-1-10000000000-112-211-1-1-1-1110-2002001100-10000
χ3222222-1222-122-12-12-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111102-2200001122-2-200110000000000-1-1-2211-1-111-1-10200-200-1-10010000
χ332222-122-1-1222222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-12022-1-1-1-10000002222-1-1-1-1-1-1-1-10002-1-10000-1-1-1-1002200000000-1-100
χ342222-122-1-1222222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-120-2-2-1-1-1-100000022-2-2-1-1-1-1-1-1-1-1000-2110000111100-2-2000000001100
χ352222-122-1-1222222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20221111000000-2-222111111110002-1-10000-1-1-1-100-2-2000000001100
χ362222-122-1-1222222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-21111000000-2-2-2-211111111000-21100001111002200000000-1-100
χ372222-122-1-1222222-1-1-12-2-1-12-1-1-122-1-2-211111122002222-1-1-1-1-2-2-2111111-202-2-1-111000000-2-222-1-1-1-11111000-2-110000-1-111002-200000000-1100
χ382222-122-1-1222222-1-1-12-2-1-12-1-1-122-1-2-211111122002222-1-1-1-1-2-2-2111111-20-22-1-111000000-2-2-2-2-1-1-1-1111100021-1000011-1-100-22000000001-100
χ392222-122-1-1222222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-2111111202-211-1-100000022221111-1-1-1-1000-2-110000-1-11100-22000000001-100
χ402222-122-1-1222222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-211111120-2211-1-100000022-2-21111-1-1-1-100021-1000011-1-1002-200000000-1100
χ4122-2-22222-22-22-2-2-2-222202-2-2-22-22-2-2000000002-22-222-2-222-2-200000000000002-2002-2002-2000022-2-200002-200002-2000000000002-2000000000
χ4222-2-22222-22-22-2-2-2-222202-2-2-22-22-2-2000000002-2-2222-2-222-2-200000000000002-200-2200-22000022-2-20000-220000-2200000000000-22000000000
χ4322-2-22222-22-22-2-2-2-222202-2-2-22-22-2-200000000-222-2-2-22222-2-20000000000000-22002-2002-20000-2-2220000-2200002-200000000000-22000000000
χ4422-2-22222-22-22-2-2-2-222202-2-2-22-22-2-200000000-22-22-2-22222-2-20000000000000-2200-2200-220000-2-22200002-20000-22000000000002-2000000000
χ4522-2-222-12-221-1-21-2-22-1-102-211-11-11-23−30033−3−32-22-2-1-111-1-11103−30033−3−300002-2002-23−3-113−300-1-11133−3−32-20000-113−3000000000-11003−300000
χ4622-2-222-12-221-1-21-2-22-1-102-211-11-11-23−30033−3−32-2-22-1-111-1-11103−30033−3−300002-200-22−331-13−300-1-11133−3−3-2200001-1−330000000001-100−3300000
χ4722-2-222-12-221-1-21-2-22-1-102-211-11-11-23−30033−3−3-222-211-1-1-1-11103−30033−3−30000-22002-23−3-11−330011-1-1−3−333-220000-113−30000000001-100−3300000
χ4822-2-222-12-221-1-21-2-22-1-102-211-11-11-23−30033−3−3-22-2211-1-1-1-11103−30033−3−30000-2200-22−331-1−330011-1-1−3−3332-200001-1−33000000000-11003−300000
χ4922-2-222-12-221-1-21-2-22-1-102-211-11-11-2−3300−3−3332-22-2-1-111-1-1110−3300−3−33300002-2002-2−33-11−3300-1-111−3−3332-20000-11−33000000000-1100−3300000
χ5022-2-222-12-221-1-21-2-22-1-102-211-11-11-2−3300−3−3332-2-22-1-111-1-1110−3300−3−33300002-200-223−31-1−3300-1-111−3−333-2200001-13−30000000001-1003−300000
χ5122-2-222-12-221-1-21-2-22-1-102-211-11-11-2−3300−3−333-222-211-1-1-1-1110−3300−3−3330000-22002-2−33-113−30011-1-133−3−3-220000-11−330000000001-1003−300000
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χ874-44-4-24-22-2-4224-2-42-21-202-2-2-1-112220000−3i3i−3i3i0000−2323−23231-11-100000−3i3i−3i3i000000−2i32i300000000003−33−3i3−i3i3−i3000000000000000000000000000000
χ884-4-44444-4-4-44-4-4-4444440-4-4-44-4-4-44400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-4-4-22-42444-2-20-4-42-2222-2400000000000023−23−2323-222-200000000000000000000000000023−23−23230000000000000000000000000000000000
χ904-4-4444-2-4-4-4-22-42444-2-20-4-42-2222-24000000000000−232323−23-222-2000000000000000000000000000−232323−230000000000000000000000000000000000
χ914-4-444-24-4-424-42-4-24-24-202224-4-42-2-20000000000000000-222-20000000000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000
χ924-4-444-24-4-424-42-4-24-24-202224-4-42-2-20000000000000000-222-200000000000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000
χ934-4-44-24422-44-4-4-44-2-2-24022-4-222-44-200−2i32i3−2i32i32i3−2i300000000-222-2000−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ944-4-44-24422-44-4-4-44-2-2-24022-4-222-44-2002i3−2i32i3−2i3−2i32i300000000-222-20002i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ954-4-44-24-222-4-22-424-2-21-202221-1-12-2-200−2i32i3i3−i3−i3i3000023−23−23231-1-11000−2i32i3i3−i3−i3i3000000000000000000−333−3−3i3i3i−3i000000000000000000000000000000
χ964-4-44-24-222-4-22-424-2-21-202221-1-12-2-200−2i32i3i3−i3−i3i30000−232323−231-1-11000−2i32i3i3−i3−i3i30000000000000000003−3−333i−3i−3i3i000000000000000000000000000000
χ974-4-44-24-222-4-22-424-2-21-202221-1-12-2-2002i3−2i3−i3i3i3−i3000023−23−23231-1-110002i3−2i3−i3i3i3−i3000000000000000000−333−33i−3i−3i3i000000000000000000000000000000
χ984-4-44-24-222-4-22-424-2-21-202221-1-12-2-2002i3−2i3−i3i3i3−i30000−232323−231-1-110002i3−2i3−i3i3i3−i30000000000000000003−3−33−3i3i3i−3i000000000000000000000000000000
χ994-4-44-2-242224-42-4-2-21-2-20-1-12-2222-2100−2i32i3−2i32i32i3−2i3000000001-1-11000i3−i3i3−i3−i3i30000000000000000−2i32i3000000000000000000i3−i33-30000000000000000
χ1004-4-44-2-242224-42-4-2-21-2-20-1-12-2222-2100−2i32i3−2i32i32i3−2i3000000001-1-11000i3−i3i3−i3−i3i300000000000000002i3−2i3000000000000000000−i3i3-330000000000000000
χ1014-4-44-2-242224-42-4-2-21-2-20-1-12-2222-21002i3−2i32i3−2i3−2i32i3000000001-1-11000−i3i3−i3i3i3−i30000000000000000−2i32i3000000000000000000i3−i3-330000000000000000
χ1024-4-44-2-242224-42-4-2-21-2-20-1-12-2222-21002i3−2i32i3−2i3−2i32i3000000001-1-11000−i3i3−i3i3i3−i300000000000000002i3−2i3000000000000000000−i3i33-30000000000000000
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
χ10588-8-8-4-48-44-4-884-8442-4-402-244-44-44-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44-44-4444422202-2-2-22-22-2-243−4300−23−23232300000000-1-1110−23230033−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44-44-4444422202-2-2-22-22-2-2−4343002323−23−2300000000-1-111023−2300−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-88444-4-44-8-4-4204-4244-4-2-2400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-484-44-8-8-48442-4-40-22-444-444-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4444-4-4442220-222-2-22-2-2-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-4444-4-4442220-222-2-22-2-2-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-8-84-4444-48-4-42044-2-444-22-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4444-4-42220-2-2-22-2-2-22200−4i34i32i3−2i3−2i32i300000000-111-10002i3−2i3−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4444-4-42220-2-2-22-2-2-222004i3−4i3−2i32i32i3−2i300000000-111-1000−2i32i3i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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