Finite Group Databasebeta

← Group #13168000

Character table — Group #13168000

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212122222666636661212121212121212124444666666666612121212121212121212121222661212121212121212121244444661212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111111111111111-1-11111111111-1-11-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111-111111-1-1-1-1111111-1-111111111-1-1-1-111-11-1-11111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-1-1111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1111-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-11-1-111111-1-1-1-11111-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-111-1-1-111-1-111-1-111-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-1-11111-1-1-1-11-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-11-11111-1-11-11-11-1-111-1-111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-11-1-1-11111-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111-1-111111111-1-1111-1-1-1-1-111-1-111-11-1-1-11111-1-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-111-11-11-1-1-1-1111-11-11-1-111-1-111-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-1-111111111111111-1-11-11-11111-1-1-1-1-11111-1-1-1-11-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-111111-1-111-111-1-111-1-111-11-11-1
χ17222222-122-1-122-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-120022222-1-1-1-1-1-1-1-1-1-10022-1-1-1-122-1-10020-1-1000020000-1-1-1-10000000
χ18222222-122-1-122-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-200222-2-211-1-1-1-1-1-1110022-1-1-1-1-2-21100-20110000-2000011110000000
χ19222222-122-1-122-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-1200-2-2-222-1-1111111-1-100-2-21111-2-2-1-10020-1-10000-2000011110000000
χ20222222-122-1-122-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-2-2-2-2-2111111111100-2-21111221100-2011000020000-1-1-1-10000000
χ21222222-122-1-122-1222-1-1-22-1-1-12-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-2-2-2111111-200-22222-1-1-1-1-1-1111100-2-2111122-1-100-20110000-20000-1-1110000000
χ22222222-122-1-122-1222-1-1-22-1-1-12-1-1-1211-2-2111122-2-2-1-1-1-1-1-1-1-1-2-2-2111111200-222-2-211-1-1-1-111-1-100-2-21111-2-2110020-1-100002000011-1-10000000
χ23222222-122-1-122-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2221111-1-1-1-1-2-2-2111111-2002-2-222-1-11111-1-1110022-1-1-1-1-2-2-1-100-201100002000011-1-10000000
χ24222222-122-1-122-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-2-2-21111112002-2-2-2-2111111-1-1-1-10022-1-1-1-122110020-1-10000-20000-1-1110000000
χ2522222-122-1222-12-12-12-12-122-1-1-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1222000-1-12200000022-1-100000000-1-122-1-1-1-1-1-1-1-1020020000-1-1-10000
χ2622222-122-1222-12-12-12-12-122-1-1-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2000-1-122000000221100000000-1-1-2-2-11-1-111110-200-200001110000
χ2722222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-22200011-2-2000000-2-2-1-10000000011221-111-1-1-1-10-200-200001110000
χ2822222-122-1222-12-12-12-12-122-1-1-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200011-2-2000000-2-2110000000011-2-211111111020020000-1-1-10000
χ2922222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-22-2000-1-122000000-2-2-1-100000000-1-12-21111-1-1110200-20000-1-110000
χ3022222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-2-22000-1-122000000-2-21100000000-1-1-221-11111-1-10-2002000011-10000
χ3122222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111122-200011-2-200000022-1-100000000112-2-11-1-1-1-1110-2002000011-10000
χ3222222-122-1222-12-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-11111111112-2200011-2-200000022110000000011-22-1-1-1-111-1-10200-20000-1-110000
χ332222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-10222-1-10000-1-1-1-1220022-1-1-1-1-1-10000-1-10200-1-1-1-1002200000000-1-100
χ342222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-10-2-22-1-10000-1-1-1-12200-2-2-1-1-1-1-1-10000110-200111100-2-2000000001100
χ352222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1022-21100001111-2-200221111110000-1-10200-1-1-1-100-2-2000000001100
χ362222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-21100001111-2-200-2-21111110000110-2001111002200000000-1-100
χ372222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111122002222-1-1-1-1-211-2-2111102-2-2-1-10000-1-1-1-1-2-200221111110000-110-200-1-111002-200000000-1100
χ382222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111122002222-1-1-1-1-211-2-211110-22-2-1-10000-1-1-1-1-2-200-2-211111100001-1020011-1-100-22000000001-100
χ392222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-2111102-221100001111220022-1-1-1-1-1-10000-110-200-1-11100-22000000001-100
χ402222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-211110-22211000011112200-2-2-1-1-1-1-1-100001-1020011-1-1002-200000000-1100
χ4122-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-2000000002-22-222-2-222-2-200000000000002-22-22-222-2-20000000000002-22-20000000000000002-2000000000
χ4222-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-2000000002-2-2222-2-222-2-200000000000002-2-22-2222-2-2000000000000-22-22000000000000000-22000000000
χ4322-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-200000000-222-2-2-22222-2-20000000000000-222-22-2-2-222000000000000-222-2000000000000000-22000000000
χ4422-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-200000000-22-22-2-22222-2-20000000000000-22-22-22-2-2220000000000002-2-220000000000000002-2000000000
χ4522-2-222-122-11-2-21-2-22-1-102-11-1-2111-23−30033−3−32-22-2-1-111-1-1110003−333−3−300002-22-2-11-1-1113−33−3000033−3−32-2-1100003−3000000000-113−30000000
χ4622-2-222-122-11-2-21-2-22-1-102-11-1-2111-23−30033−3−32-2-22-1-111-1-1110003−333−3−300002-2-221-1-1-1113−3−33000033−3−3-221-10000−330000000001-1−330000000
χ4722-2-222-122-11-2-21-2-22-1-102-11-1-2111-23−30033−3−3-222-211-1-1-1-1110003−333−3−30000-222-2-1111-1-1−333−30000−3−333-22-1100003−30000000001-1−330000000
χ4822-2-222-122-11-2-21-2-22-1-102-11-1-2111-23−30033−3−3-22-2211-1-1-1-1110003−333−3−30000-22-221-111-1-1−33−330000−3−3332-21-10000−33000000000-113−30000000
χ4922-2-222-122-11-2-21-2-22-1-102-11-1-2111-2−3300−3−3332-22-2-1-111-1-111000−33−3−33300002-22-2-11-1-111−33−330000−3−3332-2-110000−33000000000-11−330000000
χ5022-2-222-122-11-2-21-2-22-1-102-11-1-2111-2−3300−3−3332-2-22-1-111-1-111000−33−3−33300002-2-221-1-1-111−333−30000−3−333-221-100003−30000000001-13−30000000
χ5122-2-222-122-11-2-21-2-22-1-102-11-1-2111-2−3300−3−333-222-211-1-1-1-111000−33−3−3330000-222-2-1111-1-13−3−33000033−3−3-22-110000−330000000001-13−30000000
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χ804-44-44-24-42-4-4424-2-4-24-202-44222-2-4-20000000000000000-22-220000000000000000000000000000000000000000000000000000000000−2i32i300000
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χ884-4-44444-4-4-44-44-4-444440-4-4-4-444-44-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-42-2-442-444-2-20-42224-22-2-4000000000000−2i32i32i3−2i3-222-20000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ904-4-4444-2-4-42-2-442-444-2-20-42224-22-2-40000000000002i3−2i3−2i32i3-222-200000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ914-4-444-24-42-44-4-2-424-24-202-4-42-2-22420000000000000000-222-200000000000000000000000000023−23000000000000000023−23000000000000000000
χ924-4-444-24-42-44-4-2-424-24-202-4-42-2-22420000000000000000-222-2000000000000000000000000000−23230000000000000000−2323000000000000000000
χ934-4-44-2442-4-4424-4-4-2-2-240222-4-24-4-2200−2i32i3−2i32i32i3−2i300000000-222-20−2i32i300−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ944-4-44-2442-4-4424-4-4-2-2-240222-4-24-4-22002i3−2i32i3−2i3−2i32i300000000-222-202i3−2i3002i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ954-4-44-24-22-42-2242-4-2-21-202-1-12-2-221200−2i32i3i3−i3−i3i30000−2i32i32i3−2i31-1-110−2i32i300i3−i3−i3i30000000000i3−i3−i3i3000000003-3-33000000000000000000000000000000
χ964-4-44-24-22-42-2242-4-2-21-202-1-12-2-221200−2i32i3i3−i3−i3i300002i3−2i3−2i32i31-1-110−2i32i300i3−i3−i3i30000000000−i3i3i3−i300000000-333-3000000000000000000000000000000
χ974-4-44-24-22-42-2242-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i30000−2i32i32i3−2i31-1-1102i3−2i300−i3i3i3−i30000000000i3−i3−i3i300000000-333-3000000000000000000000000000000
χ984-4-44-24-22-42-2242-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i300002i3−2i3−2i32i31-1-1102i3−2i300−i3i3i3−i30000000000−i3i3i3−i3000000003-3-33000000000000000000000000000000
χ994-4-44-2-2422-442-2-42-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300000000000000000023−230000000000000000−333i−3i0000000000000000
χ1004-4-44-2-2422-442-2-42-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i3000000000000000000−232300000000000000003−3−3i3i0000000000000000
χ1014-4-44-2-2422-442-2-42-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300000000000000000023−230000000000000000−33−3i3i0000000000000000
χ1024-4-44-2-2422-442-2-42-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i3000000000000000000−232300000000000000003−33i−3i0000000000000000
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
χ10588-8-8-4-48-4-48-844-8442-4-402-44-4-2444-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-4-4-4444444222022-22-2-2-2-2-243−4300−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4-4-4444444222022-22-2-2-2-2-2−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-844484-4-4-8-4-42044-4-24-224-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4844-8-8-448-442-4-40-24-44-24-44200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44444-44-4-442220-2-22-2-2-22-2200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44444-44-4-442220-2-22-2-2-22-220000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-844-4-8-4448-4-420444-2-42-2-4400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-44-444-42220-2-2-2-222-22-200−4i34i32i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-44-444-42220-2-2-2-222-22-2004i3−4i3−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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