Finite Group Databasebeta

← Group #13168753

Character table — Group #13168753

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121222446666366612121212121212121224446666661212121212121212121212121212121244666612121212121212124444412121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1111111111111-1-1-1-1-11-1-11111-1-1-11-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-111111111-1-11111-1-1-1-11111-1-111111-111-1-1-1-1-11-1-11-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-11-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1111111111111111-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111111111-11-1-111-1-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-1-11-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1-1-11-1-1-11111-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-111-1-1-111-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-11111-1-111-1-1-1-1-1-111-1-1-1-11-11111-1-1-1-11-111111-1-11-1-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-1-1-111-1111-111-1-111-1-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-1-1-11111-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111-1-11111-1-11111-1-11111-1-1-1-111-1-11-1-111-1-1-1-11111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11-11111-1-1-1111-111-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-1-1-111-1-1111111111111-11-1-1-1-111-1-11-111111-1-11-1-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-111-1-1-1111-1
χ17222222-12-122-122-122-1-122-1-1-12-1-1-1222-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-12220-1-1-1-1-1-1220022-1-10000-1-1-1-1002-1-1-1-10-1-1000002002000000-10-100
χ18222222-12-122-122-122-1-122-1-1-12-1-1-1222-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-1-2-220-1-1-1-1-1-12200-2-2-1-10000-1-1-1-100-2111101100000-200-200000010100
χ19222222-12-122-122-122-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-122-20111111-2-200221100001111002-1-1-1-10-1-100000-200-200000010100
χ20222222-12-122-122-122-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2-2-20111111-2-200-2-2110000111100-21111011000002002000000-10-100
χ21222222-12-122-122-122-1-1-22-1-1-12-1-1-12-2-211111122002222-1-1-1-1-2-2-21111112-2-20-1-1-1-1-1-1-2-200-2-21100001111002-1-1-1101100000200-200000010-100
χ22222222-12-122-122-122-1-1-22-1-1-12-1-1-12-2-211111122002222-1-1-1-1-2-2-2111111-22-20-1-1-1-1-1-1-2-20022110000111100-2111-10-1-100000-2002000000-10100
χ23222222-12-122-122-122-1-1-22-1-1-12-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-21111112-2201111112200-2-2-1-10000-1-1-1-1002-1-1-1101100000-2002000000-10100
χ24222222-12-122-122-122-1-1-22-1-1-12-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-2111111-2220111111220022-1-10000-1-1-1-100-2111-10-1-100000200-200000010-100
χ2522222-12222-12-1-122-12-12-122-1-1-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1220200000000-1-1-1-1002222000000-12-1-12-1-1-1-1-1-1-120200-1-100000-1000
χ2622222-12222-12-1-122-12-12-122-1-1-1-12-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20200000000-1-1110022220000001-211-2-111-1-1-1-1-20-20011000001000
χ2722222-12222-12-1-122-12-12-122-1-1-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1220-20000000011-1-100-2-2-2-2000000-12-1-121-1-11111-20-20011000001000
χ2822222-12222-12-1-122-12-12-122-1-1-1-12-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-200000000111100-2-2-2-20000001-211-2111111120200-1-100000-1000
χ2922222-12222-12-1-122-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-11111111112-20-200000000-1-1110022-2-2000000-12-1-1-2111-1-11120-2001100000-1000
χ3022222-12222-12-1-122-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-220-200000000-1-1-1-10022-2-20000001-21121-1-1-1-111-20200-1-1000001000
χ3122222-12222-12-1-122-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-11111111112-20200000000111100-2-222000000-12-1-1-2-11111-1-1-20200-1-1000001000
χ3222222-12222-12-1-122-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-22020000000011-1-100-2-2220000001-2112-1-1-111-1-120-2001100000-1000
χ332222-122-12-122222-1-1-122-1-1-12-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1002222-1-1-1-1-1-1220022-1-1-1-1-1-1-1-12200000200-1-1-1-10002000-1-1-1-100000
χ342222-122-12-122222-1-1-122-1-1-12-122-1-1-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-1002-222-1-1-1-1-1-1-2-200221111-1-1-1-1-2-200000-2001111000-2000111100000
χ352222-122-12-122222-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-2-2221111-1-1-1-12-1-122-1-1-1-100-22-2-21111112200-2-2-1-1-1-11111-2-200000200-1-1-1-1000-2000111100000
χ362222-122-12-122222-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-100-2-2-2-2111111-2-200-2-2111111112200000-20011110002000-1-1-1-100000
χ372222-122-12-122222-1-1-12-2-1-1-12-122-1-111-2-211112222-1-1-1-1-1-1-1-1-211-2-2111100-2-222-1-1-1-1112200-2-2-1-11111112200000-200-1-111000-2000-1-11100000
χ382222-122-12-122222-1-1-12-2-1-1-12-122-1-111-2-2111122-2-2-1-1-1-1-1-1-1-1-211-2-2111100-2222-1-1-1-111-2-200-2-211-1-11111-2-20000020011-1-1000200011-1-100000
χ392222-122-12-122222-1-1-12-2-1-1-12-122-1-111-2-21111-2-2221111-1-1-1-1-211-2-21111002-2-2-21111-1-1220022-1-111-1-1-1-1-2-200000-200-1-111000200011-1-100000
χ402222-122-12-122222-1-1-12-2-1-1-12-122-1-111-2-21111-2-2-2-21111-1-1-1-1-211-2-211110022-2-21111-1-1-2-2002211-1-1-1-1-1-1220000020011-1-1000-2000-1-11100000
χ412-22-2222-2-22-2-22-22-22220-2-2-2-222-22-2000000002-22i−2i22-2-22-2-2200000000000002-222-2-2002i−2i00002i−2i0000002i−2i000000002i−2i0000000002i−2i0000000
χ422-22-2222-2-22-2-22-22-22220-2-2-2-222-22-2000000002-2−2i2i22-2-22-2-2200000000000002-222-2-200−2i2i0000−2i2i000000−2i2i00000000−2i2i000000000−2i2i0000000
χ432-22-2222-2-22-2-22-22-22220-2-2-2-222-22-200000000-222i−2i-2-2222-2-220000000000000-22-2-222002i−2i00002i−2i000000−2i2i000000002i−2i000000000−2i2i0000000
χ442-22-2222-2-22-2-22-22-22220-2-2-2-222-22-200000000-22−2i2i-2-2222-2-220000000000000-22-2-22200−2i2i0000−2i2i0000002i−2i00000000−2i2i0000000002i−2i0000000
χ452-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11−i3i300−i3−i3i3i32-22i−2i-1-111-111-10−i3i300−i3−i3i3i300002-2-1-111−i3i32i−2i0000−ii3−3−i3−i3i3i32i−2i00000000−ii3−30000000−ii3−300000
χ462-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11−i3i300−i3−i3i3i32-2−2i2i-1-111-111-10−i3i300−i3−i3i3i300002-2-1-111−i3i3−2i2i0000i−i−33−i3−i3i3i3−2i2i00000000i−i−330000000i−i−3300000
χ472-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11−i3i300−i3−i3i3i3-222i−2i11-1-1-111-10−i3i300−i3−i3i3i30000-2211-1-1i3−i32i−2i0000−ii3−3i3i3−i3−i3−2i2i00000000−ii3−30000000i−i−3300000
χ482-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11−i3i300−i3−i3i3i3-22−2i2i11-1-1-111-10−i3i300−i3−i3i3i30000-2211-1-1i3−i3−2i2i0000i−i−33i3i3−i3−i32i−2i00000000i−i−330000000−ii3−300000
χ492-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11i3−i300i3i3−i3−i32-22i−2i-1-111-111-10i3−i300i3i3−i3−i300002-2-1-111i3−i32i−2i0000−ii−33i3i3−i3−i32i−2i00000000−ii−330000000−ii−3300000
χ502-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11i3−i300i3i3−i3−i32-2−2i2i-1-111-111-10i3−i300i3i3−i3−i300002-2-1-111i3−i3−2i2i0000i−i3−3i3i3−i3−i3−2i2i00000000i−i3−30000000i−i3−300000
χ512-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11i3−i300i3i3−i3−i3-222i−2i11-1-1-111-10i3−i300i3i3−i3−i30000-2211-1-1−i3i32i−2i0000−ii−33−i3−i3i3i3−2i2i00000000−ii−330000000i−i3−300000
χ522-22-2-1221-2-1-2-22-221-1-120111-2-12-2-11i3−i300i3i3−i3−i3-22−2i2i11-1-1-111-10i3−i300i3i3−i3−i30000-2211-1-1−i3i3−2i2i0000i−i3−3−i3−i3i3i32i−2i00000000i−i3−30000000−ii−3300000
χ5344444-2-24-24-2-2-2-2-24-2-214-2-2-21-211-2-244-2-2-2-2-2-2000000001111-2-2-211111144000000000000-2-2000000000000-2-211-201100000000000000000000
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χ574444-24-2-2-2-24-244-2-2-21-24-211-2-2-2-21-2-2-2-2-211114400-2-2-2-211114-2-2-2-211110040-2-21111-2-20000-2-200001111000000000000000000000000000000
χ584444-24-2-2-2-24-244-2-2-21-24-211-2-2-2-21-2-2-2-2-21111-4-400222211114-2-2-2-2111100-4022-1-1-1-1220000220000-1-1-1-1000000000000000000000000000000
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χ764-44-444-2-424-424-4-2-44-2-20-42224-22-2-4000000004-40044-4-4-222-20000000000000-22-2-2220000000000000000000000000000000000000000000000
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χ834-44-4-24-222-2-424-4-22-21-202-1-12-2-22122i3−2i300−i3−i3i3i3-440022-2-21-1-1102i3−2i300−i3−i3i3i300002-2-1-111−2i32i30000000000i3i3−i3−i3000000000000000000000000000000
χ844-44-4-2-242-4-22-4-22421-2-20-12221-22-2-1−2i32i300−2i3−2i32i32i3004i−4i00001-1-110i3−i300i3i3−i3−i3000000000000−2i2i0000−2i2i23−2300000000000000i−i−330000000000000000
χ854-44-4-2-242-4-22-4-22421-2-20-12221-22-2-1−2i32i300−2i3−2i32i32i300−4i4i00001-1-110i3−i300i3i3−i3−i30000000000002i−2i00002i−2i−232300000000000000−ii3−30000000000000000
χ864-44-4-2-242-4-22-4-22421-2-20-12221-22-2-12i3−2i3002i32i3−2i3−2i3004i−4i00001-1-110−i3i300−i3−i3i3i3000000000000−2i2i0000−2i2i−232300000000000000i−i3−30000000000000000
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χ894-4-4444-2-42-44-2-4-4244-2-20-42-2-2-422240023−2323−23−232300000000-22-2200023−2323−23−232300000000000000000000000000000000000000000000000000000000
χ904-4-4444-2-42-44-2-4-4244-2-20-42-2-2-4222400−2323−232323−2300000000-22-22000−2323−232323−2300000000000000000000000000000000000000000000000000000000
χ914-4-444-24-4-4-4-2422-44-24-202-44-2222-4-20000000000000000-22-220000000000000000000000023−2300000000000000000023−2300000000000000000000
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χ954-4-444-2-2-42-4-2-22224-2-21022-212-1-12-200−2323−232323−23000000001-11-10003−33−3−330000000000000023−2300000000000000-3300−3300000000000000000000
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χ974-4-44-2442-4244-4-4-4-2-2-24022-242-4-42-2000000000000−2i32i32i3−2i3-22-22000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ984-4-44-2442-4244-4-4-4-2-2-24022-242-4-42-20000000000002i3−2i3−2i32i3-22-220000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ994-4-44-24-22224-2-4-42-2-21-202-11-2222-1-20023−23−333−30000−2i32i32i3−2i31-11-100023−23−333−3000000i3−i3−i3i30000000000003i−3i−3i3i000000000000000000000000000000
χ1004-4-44-24-22224-2-4-42-2-21-202-11-2222-1-20023−23−333−300002i3−2i3−2i32i31-11-100023−23−333−3000000−i3i3i3−i3000000000000−3i3i3i−3i000000000000000000000000000000
χ1014-4-44-24-22224-2-4-42-2-21-202-11-2222-1-200−23233−3−330000−2i32i32i3−2i31-11-1000−23233−3−33000000i3−i3−i3i3000000000000−3i3i3i−3i000000000000000000000000000000
χ1024-4-44-24-22224-2-4-42-2-21-202-11-2222-1-200−23233−3−3300002i3−2i3−2i32i31-11-1000−23233−3−33000000−i3i3i3−i30000000000003i−3i−3i3i000000000000000000000000000000
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
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χ10588-8-88-4-48-4-8444-44-8-4-420-4-44-24-2244000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-48-4844-84-4-842-4-402-444-24-44-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4-44444-444222022-2-2-2-22-2-200006i−6i6i−6i00000000-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-4-4-44444-444222022-2-2-2-22-2-20000−6i6i−6i6i00000000-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1098-88-88-4-4-84844-44-4-8-4-420444-2-42-2-4400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-444-444-44-442220-2-2-2-222-22-2−4i34i3002i32i3−2i3−2i300000000-111-102i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-444-444-44-442220-2-2-2-222-22-24i3−4i300−2i3−2i32i32i300000000-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-484-84-4844-8-42-4-40-24-4-4-2444200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4-4444-42220-2-222-2-2-2-220043−43−232323−2300000000-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4-4444-42220-2-222-2-2-2-2200−434323−23−232300000000-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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