Finite Group Databasebeta

← Group #13168386

Character table — Group #13168386

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212122444661212121212121212121212121212224444441212121266612121212121212121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11-1-1111111-1-1111111-1-111-1-1111111-1-1-11-11-1-111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111111-1111111-1-1-1-1-1111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-111-1111
χ51111111111111111111111111111111-1-11111111111111111111-111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-111111-1-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-1-11-1-111111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-11-11111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-111-111-1-11111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1111-11111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-111-11-1-111111-11-1
χ17222222-12-122-1-12222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12220220000-1-1-1-1222200220000000000-1-1-1-120-1-1-1-1-1-1000002-1-10000-1000
χ18222222-12-122-1-12222-1-1222-1-1-1-1-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-22-20-2-20000-1-111222200-2-20000000000111-1-2011-1-1-1-100000-21100001000
χ19222222-12-122-1-12222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-22022000011-1-1-2-2-2-200-2-20000000000-1-1-1120-1-1111100000-21100001000
χ20222222-12-122-1-12222-1-1222-1-1-1-1-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-20-2-200001111-2-2-2-2002200000000001111-20111111000002-1-10000-1000
χ21222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-211112-2-20220000-1-11122-2-200-2-20000000000-1-1-11-2011-1-111000002110000-1000
χ22222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-22200-1-1-1-11-21111-2-21111-2-220-2-20000-1-1-1-122-2-200220000000000111120-1-1-1-11100000-2-1-100001000
χ23222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-2111122-202200001111-2-22200220000000000-1-1-1-1-201111-1-100000-2-1-100001000
χ24222222-12-122-1-12222-1-1-222-1-1-1-1-1-12-2-2-2-200-1-1-1-11-21111-2-21111-2220-2-2000011-1-1-2-22200-2-20000000000111-120-1-111-1-1000002110000-1000
χ2522222-12-122222-12-1-12-12-1-12-12-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12022-1-1222200220000-1-10000220000002-1-10-1-1-1-10000-1-1-1-1200000-1-10-100
χ2622222-12-122222-12-1-12-12-1-12-12-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2211222200-2-20000-1-10000-2-2000000-21101-1110000-1-1-1-1-200000110100
χ2722222-12-122222-12-1-12-12-1-12-12-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1202-2-1-1-2-2-2-200220000110000-2-20000002-1-10-11-1-100001111-200000110100
χ2822222-12-122222-12-1-12-12-1-12-12-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2-211-2-2-2-200-2-2000011000022000000-2110111100001111200000-1-10-100
χ2922222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-20022-1-1-1-1-21-2-21111111120-2-2-1-122-2-200-2-20000-1-10000220000002-1-1011110000-1-111-200000-1-10100
χ3022222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-20022-1-1-1-1-21-2-211111111-202-21122-2-200220000-1-10000-2-2000000-2110-11-1-10000-1-111200000110-100
χ3122222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-21-2-21111111120-22-1-1-2-22200-2-20000110000-2-20000002-1-101-111000011-1-1200000110-100
χ3222222-12-122222-12-1-12-1-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111-202211-2-2220022000011000022000000-2110-1-1-1-1000011-1-1-200000-1-10100
χ332222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1020200-1-1-1-12200-1-1-1-12200220022-1-1-1-100020200-1-1-1-1-1-1-1-10000-1-1000000
χ342222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1020-20011112200-1-1-1-1-2-200-2-200-2-2111100020-200-1-1-1-11111000011000000
χ352222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-10-20200-1-1-1-1-2-20011112200-2-200-2-21111000-202001111-1-1-1-1000011000000
χ362222-12222-1-1222-12-1-122-1-1-12-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-10-20-2001111-2-2001111-2-200220022-1-1-1-1000-20-200111111110000-1-1000000
χ372222-12222-1-1222-12-1-12-2-1-1-12-122-1-1112222-1-1-1-1-2-211-2-21111110-20-200-1-1112200-1-11122002200-2-21111000-20-200-1-111-1-1110000-1-1000000
χ382222-12222-1-1222-12-1-12-2-1-1-12-122-1-11122-2-2-1-1-1-1-2-211-2-21111110-2020011-1-12200-1-111-2-200-2-20022-1-1-1-1000-20200-1-11111-1-1000011000000
χ392222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-222-1-1-1-1-2-211-2-2111111020-200-1-111-2-20011-1-12200-2-20022-1-1-1-100020-20011-1-1-1-111000011000000
χ402222-12222-1-1222-12-1-12-2-1-1-12-122-1-111-2-2-2-2-1-1-1-1-2-211-2-211111102020011-1-1-2-20011-1-1-2-2002200-2-211110002020011-1-111-1-10000-1-1000000
χ4122-2-2222-2-2-2-22-222-222202-2-2-2-2-222-200000022-2-2000000000000000000000000000000002-2002i−2i2i−2i2i2i−2i−2i0000000000000000002-2002i−2i0000
χ4222-2-2222-2-2-2-22-222-222202-2-2-2-2-222-200000022-2-2000000000000000000000000000000002-200−2i2i−2i2i−2i−2i2i2i0000000000000000002-200−2i2i0000
χ4322-2-2222-2-2-2-22-222-222202-2-2-2-2-222-200000022-2-200000000000000000000000000000000-22002i−2i−2i2i−2i−2i2i2i000000000000000000-22002i−2i0000
χ4422-2-2222-2-2-2-22-222-222202-2-2-2-2-222-200000022-2-200000000000000000000000000000000-2200−2i2i2i−2i2i2i−2i−2i000000000000000000-2200−2i2i0000
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χ462-22-2222-222-2-2-2-2-222220-2-2-2-222-2-22002i−2i-222-2-22000000000000000000-22002i−2i002i−2i00-2200−2i2i00000000000000002i−2i00-22000000−2i2i000000
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χ482-22-2222-222-2-2-2-2-222220-2-2-2-222-2-2200−2i2i-222-2-22000000000000000000-2200−2i2i00−2i2i00-22002i−2i0000000000000000−2i2i00-220000002i−2i000000
χ492-22-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i32i−2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i32i−2i00−ii3−32-2002i−2i00003−33−300000000−ii3−3-11−i3i30000−ii000000
χ502-22-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i32i−2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i32i−2i00−ii3−3-2200−2i2i0000−33−3300000000−ii3−31-1i3−i30000i−i000000
χ512-22-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i3−2i2i2-2-111-100−i3i300−i3i3−i3−i3i3i3000000-11−i3i3−2i2i00i−i−332-200−2i2i0000−33−3300000000i−i−33-11−i3i30000i−i000000
χ522-22-2-122-22-11-2-2-212-1-120111-2-12-21-1−i3i3−2i2i-22-111-100−i3i300−i3i3−i3−i3i3i30000001-1i3−i3−2i2i00i−i−33-22002i−2i00003−33−300000000i−i−331-1i3−i30000−ii000000
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χ864-44-4-2-2424-22-4-422-21-2-20-1-122-2-22212i3−2i300-441-1-11002i3−2i300−i3i3−i3−i3i3i30000002-2−2i32i3000000002-2000000000000000000000000-11i3−i3000000000000
χ874-4-444444-4-44-44-4-4-44440-4444-4-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-242-442-2-4-4-44-2-20-44-2-22222-4000000-22-2200000000000000000000000023−2300000000000000000000000023−2300000000000000000000
χ894-4-4444-242-442-2-4-4-44-2-20-44-2-22222-4000000-22-22000000000000000000000000−2323000000000000000000000000−232300000000000000000000
χ904-4-444-24-2-4-44-442-42-24-202-24-2-422-42000000-22-220000000000000000−2i32i3000000000000000000000000000−2i32i30000000000000000000000000
χ914-4-444-24-2-4-44-442-42-24-202-24-2-422-42000000-22-2200000000000000002i3−2i30000000000000000000000000002i3−2i30000000000000000000000000
χ924-4-444-2-2-22-442-22-42-2-2102-2-212-1-1220000001-11-100003i−3i003i−3i3i−3i0000−2i32i300000023−230000000000000000000i3−i3000−3300000000000000000000
χ934-4-444-2-2-22-442-22-42-2-2102-2-212-1-1220000001-11-100003i−3i003i−3i3i−3i00002i3−2i3000000−23230000000000000000000−i3i30003−300000000000000000000
χ944-4-444-2-2-22-442-22-42-2-2102-2-212-1-1220000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i3000000−23230000000000000000000i3−i30003−300000000000000000000
χ954-4-444-2-2-22-442-22-42-2-2102-2-212-1-1220000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i300000023−230000000000000000000−i3i3000−3300000000000000000000
χ964-4-44-2444-42-2-44-42-4-2-2402-2-242-4-422000000-22-220000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ974-4-44-2444-42-2-44-42-4-2-2402-2-242-4-422000000-22-2200000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-444-8-8-44-484-4-420-444-24-22-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-8444-448-4-8-42-40-44-24-24-42400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-484-8448-8-4-442-4-402-24444-4-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44444-44-4-4422202-2-2-2-2-222-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44444-44-4-4422202-2-2-2-2-222-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-44-48-8444-8-4-4-420444-2-42-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-4-444444-42220-2-2-2-222-2-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-4-444444-42220-2-2-2-222-2-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4844-44-4-84-8-42-404-42-4-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-4-84-4-884442-4-40-22-4-44444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444-44-44442220-2222-2-2-2-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444-44-44442220-2222-2-2-2-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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