Finite Group Databasebeta

← Group #13167961

Character table — Group #13167961

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order122233366666666633346666666661212444444366612121212121212121212121222224441212121212121212121212121212121244446666121212121212121212121212121212124441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111111111-11111-1-1-1-111111111-1-1-1-1111111-1-111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-1111-1-1111111-1-111-1-111-1-1-1-1-1-11-11111-1-111-1-11111-11-111-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-11-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111-1-1111111-1-111-1-111-1-111-1-1-1-1-1111-1-111-1-1111111-1-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-11-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-1-11-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-111-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-11-1111-1-111-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-11111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-111-1-111-1-111-1-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-11111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-1-1-111-1-1111-1111-1-11111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-12222220-1-1-1-100002222-1-1-1-10000-1-1-1-12200-1-1-1-1-1-1-1-100002000000-1-100000
χ18222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22-20-1-111000022-2-2-1-111000011112-200-1-111-1-1110000-20000001100000
χ19222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-22011-1-10000-2-22211-1-100001111-220011-1-111-1-10000-20000001100000
χ20222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2011110000-2-2-2-211110000-1-1-1-1-2-2001111111100002000000-1-100000
χ21222222-1-1-1222222-12-1-1-22-1-12-1-1-1-1211222200-1-1-1-1-2-2-2-2111111112222-2-20111100002222-1-1-1-10000-1-1-1-1-2-2001111-1-1-1-10000-20000001100000
χ22222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121122-2-200-1-1-1-1-2-2-2-211111111-2-2-2-2-22011-1-1000022-2-2-1-11100001111-220011-1-1-1-11100002000000-1-100000
χ23222222-1-1-1222222-12-1-1-22-1-12-1-1-1-1211-2-22200-1-1-1-1-2-2-2-211111111-2-2-2-22-20-1-1110000-2-22211-1-1000011112-200-1-11111-1-100002000000-1-100000
χ24222222-1-1-1222222-12-1-1-22-1-12-1-1-1-1211-2-2-2-200-1-1-1-1-2-2-2-2111111112222220-1-1-1-10000-2-2-2-211110000-1-1-1-12200-1-1-1-111110000-20000001100000
χ2522222-122222-1-12-12-12-12-12-1-12-12-1-122002222-1-1-1-12-1-1-122-1-1-1-1-1-10000022002222-1-100-1-10022002200000-12-100-1-100-1-1-1-1-1-100200-1-100000-10
χ2622222-122222-1-12-12-12-12-12-1-12-12-1-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1000002-20022-2-21100-1-1002200-2-200000-1-2100-1-100-1-1111100-200110000010
χ2722222-122222-1-12-12-12-12-12-1-12-12-1-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-100000-2200-2-222-1-1001100-2-200-2-20000012-100110011-1-1-1-100-200110000010
χ2822222-122222-1-12-12-12-12-12-1-12-12-1-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100000-2-200-2-2-2-211001100-2-20022000001-2100110011111100200-1-100000-10
χ2922222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2002222-1-1-1-1-2111-2-211111100000-2-200-2-222-1-100-1-100220022000001-21001100-1-1-1-11100-200-1-10000010
χ3022222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-20022-2-2-1-1-1-1-2111-2-211111100000-2200-2-2-2-21100-1-1002200-2-20000012-1001100-1-111-1-1002001100000-10
χ3122222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-200-2-222-1-1-1-1-2111-2-2111111000002-2002222-1-1001100-2-200-2-200000-1-2100-1-10011-1-111002001100000-10
χ3222222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-200-2-2-2-2-1-1-1-1-2111-2-211111100000220022-2-211001100-2-2002200000-12-100-1-1001111-1-100-200-1-10000010
χ332222-12222-1-122-122-1-122-1-12-1-12-12-122220022-1-1-1-1-12-1-1-1-122-1-1-1-100002022200-1-122-1-100220022000000-10-12-1-100-1-100-1-1-1-1020-1-1000000-100
χ342222-12222-1-122-122-1-122-1-12-1-12-12-1222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1000020-2220011-2-2-1-1002200-2-2000000-101-2-1-100-1-10011110-2011000000100
χ352222-12222-1-122-122-1-122-1-12-1-12-12-122-2-20022-1-1-1-1-12-1-1-1-122-1-1-1-10000-202-2-200-1-1221100-2-200-2-200000010-1211001100-1-1-1-10-2011000000100
χ362222-12222-1-122-122-1-122-1-12-1-12-12-122-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10000-20-2-2-20011-2-21100-2-20022000000101-2110011001111020-1-1000000-100
χ372222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2220022-1-1-1-11-21111-2-211110000-20-2-2-200-1-122-1-100220022000000101-21100-1-100-1-1110-20-1-1000000100
χ382222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-22200-2-2-1-1-1-11-21111-2-211110000-202-2-20011-2-2-1-1002200-2-200000010-121100-1-10011-1-102011000000-100
χ392222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-20022-1-1-1-11-21111-2-21111000020-22200-1-1221100-2-200-2-2000000-101-2-1-1001100-1-11102011000000-100
χ402222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-200-2-2-1-1-1-11-21111-2-211110000202220011-2-21100-2-20022000000-10-12-1-100110011-1-10-20-1-1000000100
χ4122-2-22222-22-22-2-2-2-22220222-2-2-2-2-2-20000000022-2-200000000000022-2-200000000000000000002-22-222-2-200000000000000000002-22-20000000
χ4222-2-22222-22-22-2-2-2-22220222-2-2-2-2-2-20000000022-2-200000000000022-2-20000000000000000000-22-2222-2-20000000000000000000-22-220000000
χ4322-2-22222-22-22-2-2-2-22220222-2-2-2-2-2-20000000022-2-2000000000000-2-22200000000000000000002-2-22-2-22200000000000000000002-2-220000000
χ4422-2-22222-22-22-2-2-2-22220222-2-2-2-2-2-20000000022-2-2000000000000-2-2220000000000000000000-222-2-2-2220000000000000000000-222-20000000
χ452-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-20000002i−2i2-2-220000000000002-22-200000002i−2i2i−2i0000000000002-22-20000000000002i−2i000000000002i−2i000
χ462-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-20000002i−2i2-2-22000000000000-22-2200000002i−2i2i−2i000000000000-22-220000000000002i−2i00000000000−2i2i000
χ472-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-2000000−2i2i2-2-220000000000002-22-20000000−2i2i−2i2i0000000000002-22-2000000000000−2i2i00000000000−2i2i000
χ482-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-2000000−2i2i2-2-22000000000000-22-220000000−2i2i−2i2i000000000000-22-22000000000000−2i2i000000000002i−2i000
χ492-2-22222-22-22-22-2-2-22220-2-2-2-222-2-22002i−2i2i−2i002-22-20000000000002-2-22000000000002i−2i2i−2i2i−2i2i−2i00002-2-22000000002i−2i2i−2i000000000000000000
χ502-2-22222-22-22-22-2-2-22220-2-2-2-222-2-22002i−2i−2i2i002-22-2000000000000-222-2000000000002i−2i−2i2i2i−2i−2i2i0000-222-2000000002i−2i−2i2i000000000000000000
χ512-2-22222-22-22-22-2-2-22220-2-2-2-222-2-2200−2i2i2i−2i002-22-2000000000000-222-200000000000−2i2i2i−2i−2i2i2i−2i0000-222-200000000−2i2i2i−2i000000000000000000
χ522-2-22222-22-22-22-2-2-22220-2-2-2-222-2-2200−2i2i−2i2i002-22-20000000000002-2-2200000000000−2i2i−2i2i−2i2i−2i2i00002-2-2200000000−2i2i−2i2i000000000000000000
χ532-2-2222-11-1-22-22-2-212-1-10-211-2-1-11123−32i−2i2i−2i00-11-1100003−33−333−3−32-2-22000−i3i3−i3i300002i−2i2i−2i−ii−ii0000-111-10000−i3i3−i3i3−ii−ii000000000003−300000
χ542-2-2222-11-1-22-22-2-212-1-10-211-2-1-11123−32i−2i−2i2i00-11-1100003−33−333−3−3-222-2000−i3i3i3−i300002i−2i−2i2i−iii−i00001-1-110000−i3i3i3−i3−iii−i00000000000−3300000
χ552-2-2222-11-1-22-22-2-212-1-10-211-2-1-11123−3−2i2i2i−2i00-11-1100003−33−333−3−3-222-2000i3−i3−i3i30000−2i2i2i−2ii−i−ii00001-1-110000i3−i3−i3i3i−i−ii00000000000−3300000
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χ582-2-2222-11-1-22-22-2-212-1-10-211-2-1-1112−332i−2i−2i2i00-11-110000−33−33−3−333-222-2000i3−i3−i3i300002i−2i−2i2i−iii−i00001-1-110000i3−i3−i3i3−iii−i000000000003−300000
χ592-2-2222-11-1-22-22-2-212-1-10-211-2-1-1112−33−2i2i2i−2i00-11-110000−33−33−3−333-222-2000−i3i3i3−i30000−2i2i2i−2ii−i−ii00001-1-110000−i3i3i3−i3i−i−ii000000000003−300000
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χ6144444-2-2-2-244-2-24-2-2-2-214-2-21-2-21-21-2-2-200440011114-2-2-2-2-2111111000004000-2-2000000-2-200-2-2000000000-20000110011000000000000000000
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χ874-44-4-2-24-4-42222-2-241-2-20-122122-2-2-1000000−4i4i1-1-11003-300003-33-3000000000002i−2i2i−2i0000000000000000000000000000−ii−3i3i00000000000000
χ884-44-4-2-24-4-42222-2-241-2-20-122122-2-2-1000000−4i4i1-1-1100-330000-33-33000000000002i−2i2i−2i0000000000000000000000000000−ii3i−3i00000000000000
χ894-4-444-24-44-442-2-42-4-24-202-4224-2-42-200004i−4i00-22-2200000000000000000000000000000−2i2i004i−4i000000000000000000−2i2i000000000000000000
χ904-4-444-24-44-442-2-42-4-24-202-4224-2-42-20000−4i4i00-22-22000000000000000000000000000002i−2i00−4i4i0000000000000000002i−2i000000000000000000
χ914-4-444-2-22-2-442-2-422-2-21022-12-212-1-223−23004i−4i001-11-1000023−23−33−3−333000000000−2i32i3000000−2i2i00−2i2i00000000000000i3−i300i−i000000000000000000
χ924-4-444-2-22-2-442-2-422-2-21022-12-212-1-223−2300−4i4i001-11-1000023−23−33−3−3330000000002i3−2i30000002i−2i002i−2i00000000000000−i3i300−ii000000000000000000
χ934-4-444-2-22-2-442-2-422-2-21022-12-212-1-2−2323004i−4i001-11-10000−23233−333−3−30000000002i3−2i3000000−2i2i00−2i2i00000000000000−i3i300i−i000000000000000000
χ944-4-444-2-22-2-442-2-422-2-21022-12-212-1-2−232300−4i4i001-11-10000−23233−333−3−3000000000−2i32i30000002i−2i002i−2i00000000000000i3−i300−ii000000000000000000
χ954-4-44-244-442-2-442-4-4-2-24022-42-242-4-2004i−4i0000-22-22000000000000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000000
χ964-4-44-244-442-2-442-4-4-2-24022-42-242-4-200−4i4i0000-22-220000000000000000000000000002i−2i00−4i4i0000000000000000002i−2i00000000000000000000
χ974-4-44-24-22-22-2-442-42-21-202-1221-2-12-223−234i−4i00001-11-10000−3323−23−3−3330000000−2i32i3000000−2i2i00−2i2i00000000000000i3−i300i−i00000000000000000000
χ984-4-44-24-22-22-2-442-42-21-202-1221-2-12-223−23−4i4i00001-11-10000−3323−23−3−33300000002i3−2i30000002i−2i002i−2i00000000000000−i3i300−ii00000000000000000000
χ994-4-44-24-22-22-2-442-42-21-202-1221-2-12-2−23234i−4i00001-11-100003−3−232333−3−300000002i3−2i3000000−2i2i00−2i2i00000000000000−i3i300i−i00000000000000000000
χ1004-4-44-24-22-22-2-442-42-21-202-1221-2-12-2−2323−4i4i00001-11-100003−3−232333−3−30000000−2i32i30000002i−2i002i−2i00000000000000i3−i300−ii00000000000000000000
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
χ10388-8-88-4-4-448-8-44-844-4-420-4-4244-24-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-4-44-448-84-84-42-40-42-44-24-2440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-488-8-44-4444-82-4-402-4-4-24444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44-44-444442220222-2-2-2-2-2-200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44-44-444442220222-2-2-2-2-2-200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-444-8-8448-4-4-4-42044-2-44-2-424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-44444-8-8-48-4-42-404-24-4-242-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444444-4-4-42220-2-2-22-2-222-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444444-4-4-42220-2-2-22-2-222-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-884-44-444-82-4-40-244-2-4-4442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-44-44-44442220-2-2-2-222-2-2243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-44-44-44442220-2-2-2-222-2-22−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000

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