Finite Group Databasebeta

← Group #13168682

Character table — Group #13168682

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444424466121212121212121212121212121222441212121266612121212121212121212121212244666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1111-1-1-1-11111-1-1111-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-111111111111111111111111-111111111111-1-111-1-1-1-1-1-11111111-11-1111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1111-1-111111111-11-1-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-11-11-1-1-1-1-1-111111-1-1-1-111-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1111-1-1-1-1111-11
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-11111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-111-11111-1-1-1-1-111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-111111-1-1-1-111-111-1-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1111-11-1-11111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-111-1-111-1-111-1-1-1-1111-1-1-1-1-111-1-111-1-11-11-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111111-11-1-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-111-1-1-1-11111-11111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-111-1-111-1-1-111-1-111-1-1-1-11
χ17222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-1220022-1-1-1-12222-1-1-1-1-1-1-1-12222202-1-1-1-122-1-12200-1-1000000-1-1-1-12-1-1020-1-1-1-1-1-1000020000-1-10000000
χ18222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-12200-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-220-2-1-1-1-1-2-21122001100000011112-1-10-20-1-111110000-20000110000000
χ19222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-1-2-20022-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-202111122-1-1-2-200-1-10000001111-21102011-1-1-1-10000-20000110000000
χ20222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-1-2-200-2-2-1-1-1-12222-1-1-1-1-1-1-1-12222-20-21111-2-211-2-20011000000-1-1-1-1-2110-20111111000020000-1-10000000
χ21222222-122-1-1222-122-1-1-22-1-12-1-1-1-1211220022-1-1-1-1-2-2-2-2111111112222-20-211-1-122-1-1220011000000-1-1-1-1-2110-20-1-1-1-1110000-20000110000000
χ22222222-122-1-1222-122-1-1-22-1-12-1-1-1-12112200-2-2-1-1-1-1-2-2-2-211111111-2-2-2-2-20211-1-1-2-2112200-1-10000001111-211020-1-111-1-1000020000-1-10000000
χ23222222-122-1-1222-122-1-1-22-1-12-1-1-1-1211-2-20022-1-1-1-1-2-2-2-211111111-2-2-2-220-2-1-11122-1-1-2-2001100000011112-1-10-2011-1-111000020000-1-10000000
χ24222222-122-1-1222-122-1-1-22-1-12-1-1-1-1211-2-200-2-2-1-1-1-1-2-2-2-2111111112222202-1-111-2-211-2-200-1-1000000-1-1-1-12-1-10201111-1-10000-20000110000000
χ2522222-12-1222-1-1222-12-12-12-1-1-12-12-122222200-1-1-1-1-12-1-1-1-122-1-1-1-1000022022220000-1-1-1-1002222000000-1-1-1-102-1-10000-1-1-1-1002-1-1000000-100
χ2622222-12-1222-1-1222-12-12-12-1-1-12-12-12222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-100002-2022220000-1-11100-2-2-2-2000000-1-1-110-2-1-10000111100-211000000100
χ2722222-12-1222-1-1222-12-12-12-1-1-12-12-122-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-10000-220-2-2-2-2000011-1-10022-2-2000000111-102110000-1-1-1-100-211000000100
χ2822222-12-1222-1-1222-12-12-12-1-1-12-12-122-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10000-2-20-2-2-2-20000111100-2-22200000011110-21100001111002-1-1000000-100
χ2922222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-2222200-1-1-1-11-21111-2-211110000-2-20-2-2220000-1-1-1-100222200000011110-2-1-10000-1-11100-2-1-1000000100
χ3022222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-222-2-200-1-1-1-11-21111-2-211110000-220-2-2220000-1-11100-2-2-2-2000000111-102-1-1000011-1-100211000000-100
χ3122222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-2-2-22200-1-1-1-11-21111-2-2111100002-2022-2-2000011-1-10022-2-2000000-1-1-110-2110000-1-11100211000000-100
χ3222222-12-1222-1-1222-12-1-2-12-1-1-12-12-1-2-2-2-2-2-200-1-1-1-11-21111-2-21111000022022-2-20000111100-2-222000000-1-1-1-10211000011-1-100-2-1-1000000100
χ332222-1222-12222-12-1-1-122-1-12-12-12-1-122002222-1-1-1-12-1-1-122-1-1-1-1-1-100000220000-1-122002222-1-1002200000002-1-100-1-1-1-1-1-1-1-10200000-1-1000-10
χ342222-1222-12222-12-1-1-122-1-12-12-12-1-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1000002-2000011-2-20022-2-2-1-100-2-2000000021-1001111-1-1-1-10-2000001100010
χ352222-1222-12222-12-1-1-122-1-12-12-12-1-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-100000-220000-1-12200-2-2221100-2-20000000-2-1100-1-1-1-111110-2000001100010
χ362222-1222-12222-12-1-1-122-1-12-12-12-1-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100000-2-2000011-2-200-2-2-2-21100220000000-21100111111110200000-1-1000-10
χ372222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-2002222-1-1-1-1-2111-2-211111100000-2-20000-1-1220022-2-2-1-100220000000-21100-1-111-1-1110-200000-1-100010
χ382222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-20022-2-2-1-1-1-1-2111-2-211111100000-22000011-2-2002222-1-100-2-20000000-2-110011-1-1-1-111020000011000-10
χ392222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-200-2-222-1-1-1-1-2111-2-2111111000002-20000-1-12200-2-2-2-21100-2-2000000021-100-1-11111-1-1020000011000-10
χ402222-1222-12222-12-1-1-12-2-1-12-12-12-1-1-2-200-2-2-2-2-1-1-1-1-2111-2-21111110000022000011-2-200-2-22211002200000002-1-10011-1-111-1-10-200000-1-100010
χ4122-2-2222-2-22-22-2-2-222220-22-2-2-2-22-220000000022-2-20000000000002i2i−2i−2i00000000000000000002-22i−2i2i2i−2i−2i00000000000000000002-2002i−2i00000
χ4222-2-2222-2-22-22-2-2-222220-22-2-2-2-22-220000000022-2-20000000000002i2i−2i−2i0000000000000000000-22−2i2i2i2i−2i−2i0000000000000000000-2200−2i2i00000
χ4322-2-2222-2-22-22-2-2-222220-22-2-2-2-22-220000000022-2-2000000000000−2i−2i2i2i00000000000000000002-2−2i2i−2i−2i2i2i00000000000000000002-200−2i2i00000
χ4422-2-2222-2-22-22-2-2-222220-22-2-2-2-22-220000000022-2-2000000000000−2i−2i2i2i0000000000000000000-222i−2i−2i−2i2i2i0000000000000000000-22002i−2i00000
χ452-22-22222-2-2-2-2-222-22220-2-2-222-2-22-200002i−2i002-2-220000000000002-22-200000000000002i−2i002i−2i00002-22-20000000000002i−2i000000000002i−2i000
χ462-22-22222-2-2-2-2-222-22220-2-2-222-2-22-200002i−2i002-2-22000000000000-22-2200000000000002i−2i002i−2i0000-22-220000000000002i−2i00000000000−2i2i000
χ472-22-22222-2-2-2-2-222-22220-2-2-222-2-22-20000−2i2i002-2-220000000000002-22-20000000000000−2i2i00−2i2i00002-22-2000000000000−2i2i00000000000−2i2i000
χ482-22-22222-2-2-2-2-222-22220-2-2-222-2-22-20000−2i2i002-2-22000000000000-22-220000000000000−2i2i00−2i2i0000-22-22000000000000−2i2i000000000002i−2i000
χ492-2-22222-22-22-22-2-2-222202-22-2-22-2-2-2002i−2i002-22-22-20000000000002i−2i−2i2i000002i−2i2-22-22i−2i00000000002i−2i−2i2i0000002i−2i2-200000000000000000000
χ502-2-22222-22-22-22-2-2-222202-22-2-22-2-2-2002i−2i00-222-22-2000000000000−2i2i2i−2i000002i−2i-22-222i−2i0000000000−2i2i2i−2i0000002i−2i-2200000000000000000000
χ512-2-22222-22-22-22-2-2-222202-22-2-22-2-2-200−2i2i002-22-22-2000000000000−2i2i2i−2i00000−2i2i2-22-2−2i2i0000000000−2i2i2i−2i000000−2i2i2-200000000000000000000
χ522-2-22222-22-22-22-2-2-222202-22-2-22-2-2-200−2i2i00-222-22-20000000000002i−2i−2i2i00000−2i2i-22-22−2i2i00000000002i−2i−2i2i000000−2i2i-2200000000000000000000
χ532-2-2222-1-221-1-22-21-22-1-1021-1-21-111-23−32i−2i002-2-11-1100003−33−333−3−32i−2i−2i2i000−i3i3−ii2-2-112i−2i003−3000000−iii−i0−i3i3000−ii-113−3000000000−i3i30000000
χ542-2-2222-1-221-1-22-21-22-1-1021-1-21-111-23−32i−2i00-22-11-1100003−33−333−3−3−2i2i2i−2i000−i3i3−ii-221-12i−2i00−33000000i−i−ii0−i3i3000−ii1-1−33000000000i3−i30000000
χ552-2-2222-1-221-1-22-21-22-1-1021-1-21-111-23−3−2i2i002-2-11-1100003−33−333−3−3−2i2i2i−2i000i3−i3i−i2-2-11−2i2i003−3000000i−i−ii0i3−i3000i−i-113−3000000000i3−i30000000
χ562-2-2222-1-221-1-22-21-22-1-1021-1-21-111-23−3−2i2i00-22-11-1100003−33−333−3−32i−2i−2i2i000i3−i3i−i-221-1−2i2i00−33000000−iii−i0i3−i3000i−i1-1−33000000000−i3i30000000
χ572-2-2222-1-221-1-22-21-22-1-1021-1-21-111-2−332i−2i002-2-11-110000−33−33−3−3332i−2i−2i2i000i3−i3−ii2-2-112i−2i00−33000000−iii−i0i3−i3000−ii-11−33000000000i3−i30000000
χ582-2-2222-1-221-1-22-21-22-1-1021-1-21-111-2−332i−2i00-22-11-110000−33−33−3−333−2i2i2i−2i000i3−i3−ii-221-12i−2i003−3000000i−i−ii0i3−i3000−ii1-13−3000000000−i3i30000000
χ592-2-2222-1-221-1-22-21-22-1-1021-1-21-111-2−33−2i2i002-2-11-110000−33−33−3−333−2i2i2i−2i000−i3i3i−i2-2-11−2i2i00−33000000i−i−ii0−i3i3000i−i-11−33000000000−i3i30000000
χ602-2-2222-1-221-1-22-21-22-1-1021-1-21-111-2−33−2i2i00-22-11-110000−33−33−3−3332i−2i−2i2i000−i3i3i−i-221-1−2i2i003−3000000−iii−i0−i3i3000i−i1-13−3000000000i3−i30000000
χ6144444-2-2-24-2-2-2-24-24-2-214-2-21-21-21-2-2-2-24400001111-24-2-211-2-211110000400-2-2-2-20000-2-200000000000000-211000110000000000000000000000
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χ704444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-2-214400-4-4001111-2-211-2-2-2-2111100000-40000000000022002200000000000202000000-1-1-1-100000000000000
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χ864-44-4-2-24-22-4-422-2421-2-20-1221-222-2-100004i−4i001-1-1100-330000-33-3300000000000000000−2i2i00−2i2i00000000000000000000i−i−3i3i00000000000000
χ874-44-4-2-24-22-4-422-2421-2-20-1221-222-2-10000−4i4i001-1-11003-300003-33-3000000000000000002i−2i002i−2i00000000000000000000−ii−3i3i00000000000000
χ884-44-4-2-24-22-4-422-2421-2-20-1221-222-2-10000−4i4i001-1-1100-330000-33-33000000000000000002i−2i002i−2i00000000000000000000−ii3i−3i00000000000000
χ894-4-444-2424-442-2-4-4-4-24-20-2-4-22242-42004i−4i0000-22-220000000000000000000004i−4i0000−2i2i00000000000000000000−2i2i0000000000000000000000
χ904-4-444-2424-442-2-4-4-4-24-20-2-4-22242-4200−4i4i0000-22-22000000000000000000000−4i4i00002i−2i000000000000000000002i−2i0000000000000000000000
χ914-4-444-2-2242-22-2-42-4-2-210-2212-1-2-12223−234i−4i00001-11-10000−3323−23−3−3330000000−2i32i3−2i2i0000−2i2i000000000000000i3−i3000i−i0000000000000000000000
χ924-4-444-2-2242-22-2-42-4-2-210-2212-1-2-12223−23−4i4i00001-11-10000−3323−23−3−33300000002i3−2i32i−2i00002i−2i000000000000000−i3i3000−ii0000000000000000000000
χ934-4-444-2-2242-22-2-42-4-2-210-2212-1-2-122−23234i−4i00001-11-100003−3−232333−3−300000002i3−2i3−2i2i0000−2i2i000000000000000−i3i3000i−i0000000000000000000000
χ944-4-444-2-2242-22-2-42-4-2-210-2212-1-2-122−2323−4i4i00001-11-100003−3−232333−3−30000000−2i32i32i−2i00002i−2i000000000000000i3−i3000−ii0000000000000000000000
χ954-4-44-244-4-2-44-442-42-2-240-2242-4-2-4220000004-4-22-2200000000000000000000000-224-4000000000000000000000000-2200000000000000000000
χ964-4-44-244-4-2-44-442-42-2-240-2242-4-2-422000000-44-22-22000000000000000000000002-2-440000000000000000000000002-200000000000000000000
χ974-4-44-24-2-4-22-2-44222-21-20-2-1-22212-1223−2300004-41-11-1000023−23−33−3−33300000000000-22-22000023−230000000000000000001-1−33000000000000000000
χ984-4-44-24-2-4-22-2-44222-21-20-2-1-22212-1223−230000-441-11-1000023−23−33−3−333000000000002-22-20000−2323000000000000000000-113−3000000000000000000
χ994-4-44-24-2-4-22-2-44222-21-20-2-1-22212-12−232300004-41-11-10000−23233−333−3−300000000000-22-220000−23230000000000000000001-13−3000000000000000000
χ1004-4-44-24-2-4-22-2-44222-21-20-2-1-22212-12−23230000-441-11-10000−23233−333−3−3000000000002-22-2000023−23000000000000000000-11−33000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-44-8-44-44-848-4-4204-4-24-2424-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-4-84-448-844-4-42-4042444-2-4-2-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48448-8-444-8-42-4-40-2-44-244-4420000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-444-44-4444-42220-22-2-2-2-22-2200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-444-44-4444-42220-22-2-2-2-22-2200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-4-844448-4-8-4-42044-2-424-2-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-48444-8-8-4-44-42-404-24-4-4-2424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-444444-4-442220-2-2-222-2-22-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-444444-4-442220-2-2-222-2-22-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-484-4-884-44-842-4-4024-4-24-444-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-44-44-444422202-22-2-22-2-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-44-44-444422202-22-2-22-2-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000

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