Finite Group Databasebeta

← Group #13168337

Character table — Group #13168337

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212224466663666121212121212121212444466666612121212121212121212121212121212441212121212121212121212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1111111-1-11-11111-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111-111111111-1-111-1-111-1-1111111-1-111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111-1-1111111111111111111-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111111111-1-11-1111-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1-11-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-111111111-1-111-1-1-1-111-1-1-1-1111-1-1-111-1-111-1-11-11-1-11111-1-11-1-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-111-11-1-11-1-111-1-1-1111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-11111-1-11-1-111-1-1-1-1111-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1111-111-1-111-11-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111-1-1111111-1-11-1-1-111-1-111-1-1-1111-111-1-111-11-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-11-1111-1-1-1-1111-1-111-1-1-1-1111-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-11111111111111-11-1-1-11111-1-1-11-1-11-1-111-1-1-111-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-11111-1-1111111-1111-1-111-1-1111-11-1-11111-1-11-1-11-1
χ17222222-12-1222-1-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1220022-1-1-1-12222-1-1-1-1-1-100-1-1-1-1220020-1-1-1-100000002000-1-1-1-100000
χ18222222-12-1222-1-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-12-20022-1-1-1-1-2-22211-1-11100-1-1-1-1-2-200-2011110000000-2000111100000
χ19222222-12-1222-1-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2221111-1-1-1-12-1-122-1-1-1-1-2200-2-2111122-2-2-1-111-1-1001111-2-20020-1-1-1-10000000-2000111100000
χ20222222-12-1222-1-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-2-200-2-21111-2-2-2-21111110011112200-20111100000002000-1-1-1-100000
χ21222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-21111112222-1-1-1-1-1-1-1-1-211-2-21111-2-20022-1-1-1-122-2-2-1-111110011112200-20-1-1110000000-2000-1-11100000
χ22222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-211111122-2-2-1-1-1-1-1-1-1-1-211-2-21111-220022-1-1-1-1-2-2-2-21111-1-1001111-2-2002011-1-10000000200011-1-100000
χ23222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2111111-2-2221111-1-1-1-1-211-2-211112-200-2-211112222-1-1-1-11100-1-1-1-1-2-200-20-1-1110000000200011-1-100000
χ24222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2111111-2-2-2-21111-1-1-1-1-211-2-211112200-2-21111-2-22211-1-1-1-100-1-1-1-122002011-1-10000000-2000-1-11100000
χ2522222-12-1222-122-12-12-12-1-12-1-122-1-1-1-122-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-12022-1-1-1-1-1-100-1-100220022-1-1-1-100-1-1020000-1-1-1-122000000000-1-1000
χ2622222-12-1222-122-12-12-12-1-12-1-122-1-1-1-122-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-120-2-2-1-1-1-1-1-100-1-1002200-2-2-1-1-1-100110-200001111-2-200000000011000
χ2722222-12-1222-122-12-12-12-1-12-1-122-1-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2022111111001100-2-20022111100-1-1020000-1-1-1-1-2-200000000011000
χ2822222-12-1222-122-12-12-12-1-12-1-122-1-1-1-122-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-2111111001100-2-200-2-2111100110-20000111122000000000-1-1000
χ2922222-12-1222-122-12-12-1-2-1-12-1-122-1-111-2-2111122002222-1-1-1-1-2-2-2111111-202-2-1-1-1-1-1-1001100-2-20022111100-110-20000-1-1112-2000000000-11000
χ3022222-12-1222-122-12-12-1-2-1-12-1-122-1-111-2-2111122002222-1-1-1-1-2-2-2111111-20-22-1-1-1-1-1-1001100-2-200-2-21111001-102000011-1-1-220000000001-1000
χ3122222-12-1222-122-12-12-1-2-1-12-1-122-1-111-2-21111-2-200-2-2-2-2-1-1-1-1-2-2-2111111202-211111100-1-100220022-1-1-1-100-110-20000-1-111-220000000001-1000
χ3222222-12-1222-122-12-12-1-2-1-12-1-122-1-111-2-21111-2-200-2-2-2-2-1-1-1-1-2-2-211111120-2211111100-1-1002200-2-2-1-1-1-1001-102000011-1-12-2000000000-11000
χ332222-12222-1-12222-1-1-122-1-1-122-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-10222000000-1-100220022-1-100000022-1-1-1-1-1-1-1-1-1-100202-1-1000000-100
χ342222-12222-1-12222-1-1-122-1-1-122-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-102-2-2000000-1-10022002211000000-2-2-11-1-1-1-1111100-20-211000000100
χ352222-12222-1-12222-1-1-122-1-1-122-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-2220000001100-2-200-2-2-1-1000000221-11111-1-1-1-100-20-211000000100
χ362222-12222-1-12222-1-1-122-1-1-122-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-20000001100-2-200-2-211000000-2-2111111111100202-1-1000000-100
χ372222-12222-1-12222-1-1-12-2-1-1-122-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-22-2000000-1-1002200-2-2-1-10000002-211-1-111-1-1110020-2-1-1000000100
χ382222-12222-1-12222-1-1-12-2-1-1-122-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-2-22000000-1-1002200-2-211000000-221-1-1-11111-1-100-20211000000-100
χ392222-12222-1-12222-1-1-12-2-1-1-122-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111022-20000001100-2-20022-1-10000002-2-1111-1-1-1-11100-20211000000-100
χ402222-12222-1-12222-1-1-12-2-1-1-122-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111102-220000001100-2-2002211000000-22-1-111-1-111-1-10020-2-1-1000000100
χ4122-2-22222-22-2-22-2-2-222202-2-22-22-2-2-2000000002-22-222-2-222-2-200000000000002-222-2-22-2002-200000000002-200002-200000000000002-20000000
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χ4622-2-222-1212-2-2-11-2-22-1-102-21-11-111-2003−333−3−32-2-22-1-111-1-11103−30033−3−300002-2-1-111-22001-13−3−330033−3−3-2200001-1−33000000000001-1−3300000
χ4722-2-222-1212-2-2-11-2-22-1-102-21-11-111-2003−333−3−3-222-211-1-1-1-11103−30033−3−30000-2211-1-12-200-11−333−300−3−333-220000-113−3000000000001-1−3300000
χ4822-2-222-1212-2-2-11-2-22-1-102-21-11-111-2003−333−3−3-22-2211-1-1-1-11103−30033−3−30000-2211-1-1-22001-1−33−3300−3−3332-200001-1−3300000000000-113−300000
χ4922-2-222-1212-2-2-11-2-22-1-102-21-11-111-200−33−3−3332-22-2-1-111-1-1110−3300−3−33300002-2-1-1112-200-11−33−3300−3−3332-20000-11−3300000000000-11−3300000
χ5022-2-222-1212-2-2-11-2-22-1-102-21-11-111-200−33−3−3332-2-22-1-111-1-1110−3300−3−33300002-2-1-111-22001-1−333−300−3−333-2200001-13−3000000000001-13−300000
χ5122-2-222-1212-2-2-11-2-22-1-102-21-11-111-200−33−3−333-222-211-1-1-1-1110−3300−3−3330000-2211-1-12-200-113−3−330033−3−3-220000-11−33000000000001-13−300000
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χ884-4-44444-4-4-4-44-44-444440-4-4-4-4-4-444400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-42-4-442-2-444-2-20-4-42222-2-24000000000000−2i32i32i3−2i3-222-2000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ904-4-4444-2-42-4-442-2-444-2-20-4-42222-2-240000000000002i3−2i3−2i32i3-222-20000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ914-4-444-242-4-4-4-2-4424-24-2022-422-44-2-2−2i32i300−2i32i32i3−2i300000000-222-2000−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ924-4-444-242-4-4-4-2-4424-24-2022-422-44-2-22i3−2i3002i3−2i3−2i32i300000000-222-20002i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ934-4-444-2-222-4-4-22-224-2-210222-1-12-21-2−2i32i300i3−i3−i3i30000−2i32i32i3−2i31-1-11000−2i32i3i3−i3−i3i3000000i3−i3−i3i30000000000003-3-33000000000000000000000000000000
χ944-4-444-2-222-4-4-22-224-2-210222-1-12-21-2−2i32i300i3−i3−i3i300002i3−2i3−2i32i31-1-11000−2i32i3i3−i3−i3i3000000−i3i3i3−i3000000000000-333-3000000000000000000000000000000
χ954-4-444-2-222-4-4-22-224-2-210222-1-12-21-22i3−2i300−i3i3i3−i30000−2i32i32i3−2i31-1-110002i3−2i3−i3i3i3−i3000000i3−i3−i3i3000000000000-333-3000000000000000000000000000000
χ964-4-444-2-222-4-4-22-224-2-210222-1-12-21-22i3−2i300−i3i3i3−i300002i3−2i3−2i32i31-1-110002i3−2i3−i3i3i3−i3000000−i3i3i3−i30000000000003-3-33000000000000000000000000000000
χ974-4-44-244-4-4224-44-4-2-2-240222-4-42-24-20000000000000000-222-200000000000000000000000000000−2i32i300000000000000−2i32i3000000000000000000
χ984-4-44-244-4-4224-44-4-2-2-240222-4-42-24-20000000000000000-222-2000000000000000000000000000002i3−2i3000000000000002i3−2i3000000000000000000
χ994-4-44-2-242-422-2-442-21-2-20-1-12222-2-21−2i32i300−2i32i32i3−2i3000000001-1-11000i3−i3i3−i3−i3i300000000000000000000−2i32i300000000000000i3−i33-30000000000000000
χ1004-4-44-2-242-422-2-442-21-2-20-1-12222-2-21−2i32i300−2i32i32i3−2i3000000001-1-11000i3−i3i3−i3−i3i3000000000000000000002i3−2i300000000000000−i3i3-330000000000000000
χ1014-4-44-2-242-422-2-442-21-2-20-1-12222-2-212i3−2i3002i3−2i3−2i32i3000000001-1-11000−i3i3−i3i3i3−i300000000000000000000−2i32i300000000000000i3−i3-330000000000000000
χ1024-4-44-2-242-422-2-442-21-2-20-1-12222-2-212i3−2i3002i3−2i3−2i32i3000000001-1-11000−i3i3−i3i3i3−i3000000000000000000002i3−2i300000000000000−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
χ10588-8-8-4-48-4-8-4448-8442-4-402-24-44-444-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44-444-444422202-2-22-22-2-2-20043−43−23−23232300000000-1-1110−23230033−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44-444-444422202-2-22-22-2-2-200−43432323−23−2300000000-1-111023−2300−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-4-8-44-4-84484-42-404-424-4-2-24400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-48484-44-8-8-442-4-40-22-44-4444-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-44-4444-442220-222-22-2-2-2-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-44-4444-442220-222-22-2-2-2-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4-844484-4-8-4-42-4044-244-22-4-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44444-44-44-42220-2-2-2-2-2-2222−4i34i3002i3−2i3−2i32i300000000-111-10002i3−2i3−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44444-44-44-42220-2-2-2-2-2-22224i3−4i300−2i32i32i3−2i300000000-111-1000−2i32i3i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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