Finite Group Databasebeta

← Group #13168299

Character table — Group #13168299

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121222441212121236661212121212121212124444666612121212121212121212121212121212121244661212121212121212121224444661212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111111111111-1-111111111111111-1-11-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111-1111-1-1-1-11111-1-1111111111111-1-1-1-111-11-1-11111-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-1-11-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-11-1-111111-1-1-1-11111-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-11111-1-1-1-111111-1-1-1-1-111-1-1-1-111-1-1-11111-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-11-1-11-1-111-1-11-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-1-111-1-11-11-1111-1-111-1-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-111-11-11-1-1-1-11111-11-111-1-1-1-111-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11-11-11111-1-111-11-111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1111-11-1111-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1111111-1-1-1-1111111-1-11-11-11111-1-1-11-1-11-1-111-1-11-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-111111-1-111-1-111-1-1-11111-11-11-1
χ17222222-122-1-122-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200222-1-1-1-122-1-10022-1-1-1-1-1-1-1-122-1-10020-1-1000020000-1-1-1-10000000
χ18222222-122-1-122-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-1200-222-1-111-2-2-1-100-2-211111111-2-2-1-10020-1-10000-2000011110000000
χ19222222-122-1-122-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2002-2-211-1-122110022-1-1-1-1-1-1-1-1-2-21100-20110000-2000011110000000
χ20222222-122-1-122-1222-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-2-2-21111-2-21100-2-211111111221100-2011000020000-1-1-1-10000000
χ21222222-122-1-122-1222-1-1-22-12-1-1-1-1-12-2-21111112222-1-1-1-1-1-1-1-1-2-2-2111111-200-222-1-111221100-2-2-1-1-1-1111122-1-100-20110000-2000011-1-10000000
χ22222222-122-1-122-1222-1-1-22-12-1-1-1-1-12-2-211111122-2-21111-1-1-1-1-2-2-2111111-200222-1-1-1-1-2-21100221111-1-1-1-1-2-2-1-100-2011000020000-1-1110000000
χ23222222-122-1-122-1222-1-1-22-12-1-1-1-1-12-2-2111111-2-222-1-1-1-1-1-1-1-1-2-2-2111111200-2-2-2111122-1-100-2-2-1-1-1-11111-2-2110020-1-1000020000-1-1110000000
χ24222222-122-1-122-1222-1-1-22-12-1-1-1-1-12-2-2111111-2-2-2-21111-1-1-1-1-2-2-21111112002-2-211-1-1-2-2-1-100221111-1-1-1-122110020-1-10000-2000011-1-10000000
χ2522222-12-12222-12-12-12-12-1-1-12-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12220-1-122000022-1-1000000000000-1-122-1-1-1-1-1-1-1-1022000000-1-1-10000
χ2622222-12-12222-12-12-12-12-1-1-12-122-1-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-20-1-12200002211000000000000-1-1-2-2-11-1-111110-2-20000001110000
χ2722222-12-12222-12-12-12-12-1-1-12-122-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-222011-2-20000-2-2-1-100000000000011221-111-1-1-1-10-2-20000001110000
χ2822222-12-12222-12-12-12-12-1-1-12-122-1-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2011-2-20000-2-21100000000000011-2-211111111022000000-1-1-10000
χ2922222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-22-20-1-1220000-2-2-1-1000000000000-1-12-21111-1-1110-22000000-1-110000
χ3022222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-2-220-1-1220000-2-211000000000000-1-1-221-11111-1-102-200000011-10000
χ3122222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111122-2011-2-2000022-1-1000000000000112-2-11-1-1-1-11102-200000011-10000
χ3222222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-22011-2-20000221100000000000011-22-1-1-1-111-1-10-22000000-1-110000
χ332222-1222-122-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100222222-1-1-1-12-1-122-1-1-1-10222000022-1-10022-1-1-1-1-1-1-1-1-1-10000-1-10200-1-1-1-1000220000000-1-100
χ342222-1222-122-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100222222-1-1-1-12-1-122-1-1-1-10-2-22000022-1-100-2-2-1-1-1-1-1-1-1-1-1-10000110-2001111000-2-200000001100
χ352222-1222-122-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1022-20000-2-211002211111111110000-1-10200-1-1-1-1000-2-200000001100
χ362222-1222-122-1222-1-1-122-12-1-12-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-20000-2-21100-2-211111111110000110-2001111000220000000-1-100
χ372222-1222-122-1222-1-1-12-2-12-1-12-1-12-111-2-2111100222222-1-1-1-1-211-2-2111102-2-20000-2-2-1-1002211-1-1-1-111110000-110-200-1-1110002-20000000-1100
χ382222-1222-122-1222-1-1-12-2-12-1-12-1-12-111-2-2111100222222-1-1-1-1-211-2-211110-22-20000-2-2-1-100-2-211-1-1-1-1111100001-1020011-1-1000-2200000001-100
χ392222-1222-122-1222-1-1-12-2-12-1-12-1-12-111-2-2111100-2-2-2-2-2-2-1-1-1-1-211-2-2111102-22000022110022-1-11111-1-1-1-10000-110-200-1-111000-2200000001-100
χ402222-1222-122-1222-1-1-12-2-12-1-12-1-12-111-2-2111100-2-2-2-2-2-2-1-1-1-1-211-2-211110-2220000221100-2-2-1-11111-1-1-1-100001-1020011-1-10002-20000000-1100
χ412-2-222222-2-22-2-2-2-22222022-2-2-22-2-2-2000000002-22i−2i2i2i−2i−2i22-2-200000000000002-22-2002i−2i0000002i2i−2i−2i00002i−2i2-2000000000000000002i−2i0000000
χ422-2-222222-2-22-2-2-2-22222022-2-2-22-2-2-2000000002-2−2i2i−2i−2i2i2i22-2-200000000000002-22-200−2i2i000000−2i−2i2i2i0000−2i2i2-200000000000000000−2i2i0000000
χ432-2-222222-2-22-2-2-2-22222022-2-2-22-2-2-200000000-222i−2i2i2i−2i−2i22-2-20000000000000-22-22002i−2i0000002i2i−2i−2i0000−2i2i-2200000000000000000−2i2i0000000
χ442-2-222222-2-22-2-2-2-22222022-2-2-22-2-2-200000000-22−2i2i−2i−2i2i2i22-2-20000000000000-22-2200−2i2i000000−2i−2i2i2i00002i−2i-22000000000000000002i−2i0000000
χ452-2-2222-12-21-1-2-21-222-1-102-1-211-111-2003−333−3−32-22i−2i−i−iii-1-1110003−333−3−300002-2-11−i3i32i−2i3−30000−i−iii−i3−i3i3i32i−2i-1100003−3000000000−i3i3−ii0000000
χ462-2-2222-12-21-1-2-21-222-1-102-1-211-111-2003−333−3−32-2−2i2iii−i−i-1-1110003−333−3−300002-2-11i3−i3−2i2i3−30000ii−i−ii3i3−i3−i3−2i2i-1100003−3000000000i3−i3i−i0000000
χ472-2-2222-12-21-1-2-21-222-1-102-1-211-111-2003−333−3−3-222i−2i−i−iii-1-1110003−333−3−30000-221-1−i3i32i−2i−330000−i−iii−i3−i3i3i3−2i2i1-10000−33000000000i3−i3i−i0000000
χ482-2-2222-12-21-1-2-21-222-1-102-1-211-111-2003−333−3−3-22−2i2iii−i−i-1-1110003−333−3−30000-221-1i3−i3−2i2i−330000ii−i−ii3i3−i3−i32i−2i1-10000−33000000000−i3i3−ii0000000
χ492-2-2222-12-21-1-2-21-222-1-102-1-211-111-200−33−3−3332-22i−2i−i−iii-1-111000−33−3−33300002-2-11i3−i32i−2i−330000−i−iiii3i3−i3−i32i−2i-110000−33000000000i3−i3−ii0000000
χ502-2-2222-12-21-1-2-21-222-1-102-1-211-111-200−33−3−3332-2−2i2iii−i−i-1-111000−33−3−33300002-2-11−i3i3−2i2i−330000ii−i−i−i3−i3i3i3−2i2i-110000−33000000000−i3i3i−i0000000
χ512-2-2222-12-21-1-2-21-222-1-102-1-211-111-200−33−3−333-222i−2i−i−iii-1-111000−33−3−3330000-221-1i3−i32i−2i3−30000−i−iiii3i3−i3−i3−2i2i1-100003−3000000000−i3i3i−i0000000
χ522-2-2222-12-21-1-2-21-222-1-102-1-211-111-200−33−3−333-22−2i2iii−i−i-1-111000−33−3−3330000-221-1−i3i3−2i2i3−30000ii−i−i−i3−i3i3i32i−2i1-100003−3000000000i3−i3−ii0000000
χ5344444-2-2-24-2-24-2-2-24-2-214-21-2-21-2-21-244-2-2-2-2-2-2440000001111-2-2-21111114000-2-2-2-20000-2-2000000000000001100-201100000000000000000000
χ5444444-2-2-24-2-24-2-2-24-2-214-21-2-21-2-21-244-2-2-2-2-2-2-4-40000001111-2-2-2111111-4000222200002200000000000000-1-10020-1-100000000000000000000
χ5544444-2-2-24-2-24-2-2-24-2-21-4-21-2-21-2-21-2-4-4222222440000001111222-1-1-1-1-1-1-4000-2-2-2-200002200000000000000110020-1-100000000000000000000
χ5644444-2-2-24-2-24-2-2-24-2-21-4-21-2-21-2-21-2-4-4222222-4-40000001111222-1-1-1-1-1-1400022220000-2-200000000000000-1-100-201100000000000000000000
χ574444-24-24-2-2-2-24-24-2-21-24-2-2-21-211-2-2-2-2-2-211110044-2-2-2-211114-2-2-2-2111100040000-2-2-2-20000-2-211111111000000000000000000000000000000
χ584444-24-24-2-2-2-24-24-2-21-24-2-2-21-211-2-2-2-2-2-2111100-4-4222211114-2-2-2-21111000-400002222000022-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-24-2-2-2-24-24-2-21-2-4-2-2-21-211-2-22222-1-1-1-10044-2-2-2-21111-42222-1-1-1-1000-4000022-2-20000221111-1-1-1-1000000000000000000000000000000
χ604444-24-24-2-2-2-24-24-2-21-2-4-2-2-21-211-2-22222-1-1-1-100-4-422221111-42222-1-1-1-100040000-2-2220000-2-2-1-1-1-11111000000000000000000000000000000
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χ7444-4-4-24-2-4-2-22242-42-21-2022-21-2-1-1222i3−2i300−i3i3−i3i3000023−2323−231-1-1102i3−2i300−i3i3−i3i3000000000000000000−33−33−3i3i−3i3i000000000000000000000000000000
χ7544-4-4-24-2-4-2-22242-42-21-2022-21-2-1-1222i3−2i300−i3i3−i3i30000−2323−23231-1-1102i3−2i300−i3i3−i3i30000000000000000003−33−33i−3i3i−3i000000000000000000000000000000
χ7644-4-4-2-242-24-42-2-4221-2-20-121-2-2222-1−2i32i300−2i32i3−2i32i3000000001-1-110i3−i300i3−i3i3−i30000000000000023−2300000000000000000000−333i−3i0000000000000000
χ7744-4-4-2-242-24-42-2-4221-2-20-121-2-2222-1−2i32i300−2i32i3−2i32i3000000001-1-110i3−i300i3−i3i3−i300000000000000−2323000000000000000000003−3−3i3i0000000000000000
χ7844-4-4-2-242-24-42-2-4221-2-20-121-2-2222-12i3−2i3002i3−2i32i3−2i3000000001-1-110−i3i300−i3i3−i3i30000000000000023−2300000000000000000000−33−3i3i0000000000000000
χ7944-4-4-2-242-24-42-2-4221-2-20-121-2-2222-12i3−2i3002i3−2i32i3−2i3000000001-1-110−i3i300−i3i3−i3i300000000000000−2323000000000000000000003−33i−3i0000000000000000
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χ834-44-44-242-4-4-4424-2-4-24-20222-42-44-2-20000000000000000-22-220000000000000000000000000000000000000000000000000000000000−2i32i300000
χ844-44-44-242-4-4-4424-2-4-24-20222-42-44-2-20000000000000000-22-2200000000000000000000000000000000000000000000000000000000002i3−2i300000
χ854-44-4-244-42-4-4-2-4442-2-2402-422-42-24-20000000000000000-22-22000000000000000000000000023−23000023−23−2323000000000000000000000000000000
χ864-44-4-244-42-4-4-2-4442-2-2402-422-42-24-20000000000000000-22-220000000000000000000000000−23230000−232323−23000000000000000000000000000000
χ874-44-4-24-2-4222-2-4-242-21-20222-12-11-2-200003i−3i−3i3i0000−2i32i32i3−2i31-11-1000003i−3i−3i3i0000000000000000−2323i3−i3−i3i33−3−33000000000000000000000000000000
χ884-44-4-24-2-4222-2-4-242-21-20222-12-11-2-200003i−3i−3i3i00002i3−2i3−2i32i31-11-1000003i−3i−3i3i000000000000000023−23−i3i3i3−i3−333−3000000000000000000000000000000
χ894-44-4-24-2-4222-2-4-242-21-20222-12-11-2-20000−3i3i3i−3i0000−2i32i32i3−2i31-11-100000−3i3i3i−3i000000000000000023−23i3−i3−i3i3−333−3000000000000000000000000000000
χ904-44-4-24-2-4222-2-4-242-21-20222-12-11-2-20000−3i3i3i−3i00002i3−2i3−2i32i31-11-100000−3i3i3i−3i0000000000000000−2323−i3i3i3−i33−3−33000000000000000000000000000000
χ914-4-444-24-2-4-44-42-424-24-20-2-22-424-422000000004-4000000-2-2220000000000000-224-400000000000000000000-2200000000000000000000000000
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χ944-4-444-2-2-2-42-2-42224-2-210-2122-1-22-120023−232323−23−23-4400000011-1-1000−33−3−33300002-22-20000−232300000000000000-1100003−300000000000000000000
χ954-4-444-2-2-2-42-2-42224-2-210-2122-1-22-1200−2323−23−2323234-400000011-1-10003−333−3−30000-22-220000−2323000000000000001-100003−300000000000000000000
χ964-4-444-2-2-2-42-2-42224-2-210-2122-1-22-1200−2323−23−232323-4400000011-1-10003−333−3−300002-22-2000023−2300000000000000-110000−3300000000000000000000
χ974-4-44-24442-442-4-4-4-2-2-240-2422-4-22-4200000000004i−4i4i4i−4i−4i-2-2220000000000000000000−2i2i000000−2i−2i2i2i0000000000000000000000000000000000
χ984-4-44-24442-442-4-4-4-2-2-240-2422-4-22-420000000000−4i4i−4i−4i4i4i-2-22200000000000000000002i−2i0000002i2i−2i−2i0000000000000000000000000000000000
χ994-4-44-24-2422-22-42-4-2-21-20-2-22-121-1220023−23−3−333004i−4i−2i−2i2i2i11-1-100023−23−3−33300000000−2i32i3−2i2i000000ii−i−ii3i3−i3−i3000000000000000000000000000000
χ1004-4-44-24-2422-22-42-4-2-21-20-2-22-121-1220023−23−3−33300−4i4i2i2i−2i−2i11-1-100023−23−3−333000000002i3−2i32i−2i000000−i−iii−i3−i3i3i3000000000000000000000000000000
χ1014-4-44-24-2422-22-42-4-2-21-20-2-22-121-12200−232333−3−3004i−4i−2i−2i2i2i11-1-1000−232333−3−3000000002i3−2i3−2i2i000000ii−i−i−i3−i3i3i3000000000000000000000000000000
χ1024-4-44-24-2422-22-42-4-2-21-20-2-22-121-12200−232333−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−300000000−2i32i32i−2i000000−i−iiii3i3−i3−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
χ10588-8-88-4-448-44-8-444-8-4-4204-2-4-4244-2400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-444-44442220-2-2222-2-2-2-2−4i34i3002i3−2i32i3−2i300000000-111-102i3−2i300−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4-444-44442220-2-2222-2-2-2-24i3−4i300−2i32i3−2i32i300000000-111-10−2i32i300i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-44-84484-4-4-8-4-4204-244-24-42-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4844-8-8-448-442-4-40-24-2444-4-4200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44444-44-4-442220-2-2-2-2-2-222200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44444-44-4-442220-2-2-2-2-2-22220000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-44-8844-84-42-4-402-4-244-444-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-444-44444-4222022-2-2-22-2-2-20043−43−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-444-44444-4222022-2-2-22-2-2-200−43432323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000

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