Finite Group Databasebeta

← Group #13169350

Character table — Group #13169350

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666663334666666666121244444436661212121212121212121212124444444121212121212121212121212121212122244121212121212121212121212121212121212121244466121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111111-11-1-11111111111-1-111-1-1-1-11111-111-1-1-1-1-111111111-11-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-111-1111111-1-1-1-1-1-11111-1-111-1-1-1-11-1111111-1-1-1-111111-1-1-1-111-1-1-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-111-1111111111-1-1-1-1-1-1111-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-111-1-111-1-111-1-111-1-1-1-111111-1-11-1-11111-1-111-1-11-11-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-11111-1-111-1-1-1-1-11-1-111-1-1-1-11111-1-1-111-1-11111-1-11-11
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-11111-1-111-111-1-11111-11-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-11111-111-1-111-1-1-111
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11-111-1-11111-1-1-1-111-111-1-11111111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-111-1-111-1-111-1-1-1-1-1-11111-111-111-1-1-1-111-1-1111-11-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-1-12-12222-122-1-1222-1-1-1-1-1-1222002222-1-1-1-1-12-1-1-1-122-1-1-1-100000222200002222-1-1-1-10022000000-1-102-1-1-1-1-1-1-1-10000002-1-1000000-100
χ18222222-1-12-12222-122-1-1222-1-1-1-1-1-12220022-2-2-1-1-1-1-12-1-1-1-122-1-1-1-100000-22-2-200002222-1-11100-2-20000001-10-21111-1-1-1-1000000-211000000100
χ19222222-1-12-12222-122-1-1222-1-1-1-1-1-122200-2-222-1-1-1-1-12-1-1-1-122-1-1-1-1000002-2220000-2-2-2-211-1-100-2-2000000-1102-1-1-1-11111000000-211000000100
χ20222222-1-12-12222-122-1-1222-1-1-1-1-1-122200-2-2-2-2-1-1-1-1-12-1-1-1-122-1-1-1-100000-2-2-2-20000-2-2-2-211110022000000110-2111111110000002-1-1000000-100
χ21222222-1-12-12222-122-1-1-222-1-1-1-1-1-12-2-2002222-1-1-1-11-21111-2-2111100000-2-222000022-2-2-1-1-1-10022000000110-2-1-111-1-111000000-2-1-1000000100
χ22222222-1-12-12222-122-1-1-222-1-1-1-1-1-12-2-20022-2-2-1-1-1-11-21111-2-21111000002-2-2-2000022-2-2-1-11100-2-2000000-110211-1-1-1-111000000211000000-100
χ23222222-1-12-12222-122-1-1-222-1-1-1-1-1-12-2-200-2-222-1-1-1-11-21111-2-2111100000-22220000-2-22211-1-100-2-20000001-10-2-1-11111-1-1000000211000000-100
χ24222222-1-12-12222-122-1-1-222-1-1-1-1-1-12-2-200-2-2-2-2-1-1-1-11-21111-2-211110000022-2-20000-2-22211110022000000-1-10211-1-111-1-1000000-2-1-1000000100
χ2522222-12222-12-1-122-12-12-1-12-1-122-1-1-1-1222200-1-1-1-122-1-122-1-1-1-1-1-1222220200-1-1-1-1-1-1-1-12200220000-1-1-1-102200000-1-1-1-1-1-1-1-10200000-1-100000
χ2622222-12222-12-1-122-12-12-1-12-1-122-1-1-1-122-2-200-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-220-200-1-1-1-11111-2-20022000011110-22000001111-1-1-1-10-2000001100000
χ2722222-12222-12-1-122-12-12-1-12-1-122-1-1-1-1-2-22200-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-2-202001111-1-1-1-12200-2-20000111102-200000-1-1-1-111110-2000001100000
χ2822222-12222-12-1-122-12-12-1-12-1-122-1-1-1-1-2-2-2-200-1-1-1-122-1-122-1-1-1-1-1-12222-20-20011111111-2-200-2-20000-1-1-1-10-2-200000111111110200000-1-100000
χ2922222-12222-12-1-122-12-1-2-1-12-1-122-1-111222200-1-1-1-1-2-211-2-21111112222-20-200-1-111-1-1112200220000-1-1-1-10-2-200000-1-111-1-1110-2000001100000
χ3022222-12222-12-1-122-12-1-2-1-12-1-122-1-11122-2-200-1-1-1-1-2-211-2-2111111-2-2-2-2-20200-1-11111-1-1-2-200220000111102-20000011-1-1-1-1110200000-1-100000
χ3122222-12222-12-1-122-12-1-2-1-12-1-122-1-111-2-22200-1-1-1-1-2-211-2-2111111-2-2-2-220-20011-1-1-1-1112200-2-2000011110-2200000-1-11111-1-10200000-1-100000
χ3222222-12222-12-1-122-12-1-2-1-12-1-122-1-111-2-2-2-200-1-1-1-1-2-211-2-211111122222020011-1-111-1-1-2-200-2-20000-1-1-1-10220000011-1-111-1-10-2000001100000
χ332222-1222-122-1222-1-1-122-1-1-122-1-12-122220022-1-1-1-12-122-1-1-1-1-1-1-1-10000220-1-1222200000022-1-10022000020-1-1-1-1-1-10000-1-1-1-120000-1-100000-10
χ342222-1222-122-1222-1-1-122-1-1-122-1-12-1222200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-100002-20112222000000-2-2-1-100-2-20000-20-1111110000-1-1-1-1-20000110000010
χ352222-1222-122-1222-1-1-122-1-1-122-1-12-122-2-20022-1-1-1-12-122-1-1-1-1-1-1-1-10000-220-1-1-2-2-2-2000000221100-2-20000201-1-1-1-1-100001111-20000110000010
χ362222-1222-122-1222-1-1-122-1-1-122-1-12-122-2-200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10000-2-2011-2-2-2-2000000-2-21100220000-201111110000111120000-1-100000-10
χ372222-1222-122-1222-1-1-12-2-1-1-122-1-12-1-2-2220022-1-1-1-1-21-2-2111111110000-2-20-1-122-2-200000022-1-100220000-2011-1-1110000-1-111-20000-1-10000010
χ382222-1222-122-1222-1-1-12-2-1-1-122-1-12-1-2-22200-2-2-1-1-1-1-21-2-2111111110000-2201122-2-2000000-2-2-1-100-2-20000201-111-1-10000-1-111200001100000-10
χ392222-1222-122-1222-1-1-12-2-1-1-122-1-12-1-2-2-2-20022-1-1-1-1-21-2-21111111100002-20-1-1-2-222000000221100-2-20000-20-11-1-111000011-1-1200001100000-10
χ402222-1222-122-1222-1-1-12-2-1-1-122-1-12-1-2-2-2-200-2-2-1-1-1-1-21-2-211111111000022011-2-222000000-2-2110022000020-1-111-1-1000011-1-1-20000-1-10000010
χ4122-2-22222-2-2-222-2-2-222202-222-2-2-2-2-20000000022-2-200000000000022-2-200000000000000000002-22-222-2-200000000000000000002-22-20000000
χ4222-2-22222-2-2-222-2-2-222202-222-2-2-2-2-20000000022-2-200000000000022-2-20000000000000000000-22-2222-2-20000000000000000000-22-220000000
χ4322-2-22222-2-2-222-2-2-222202-222-2-2-2-2-20000000022-2-2000000000000-2-22200000000000000000002-2-22-2-22200000000000000000002-2-220000000
χ4422-2-22222-2-2-222-2-2-222202-222-2-2-2-2-20000000022-2-2000000000000-2-2220000000000000000000-222-2-2-2220000000000000000000-222-20000000
χ452-22-2222-2-222-2-2-2-222220-2-2-2-22-22-22002-22i−2i002-2-220000000000002i−2i2i−2i000002-2002i−2i002i−2i002-200002i−2i2i−2i000000002i−2i002-20000000000000000
χ462-22-2222-2-222-2-2-2-222220-2-2-2-22-22-22002-2−2i2i002-2-22000000000000−2i2i−2i2i000002-200−2i2i00−2i2i002-20000−2i2i−2i2i00000000−2i2i002-20000000000000000
χ472-22-2222-2-222-2-2-2-222220-2-2-2-22-22-2200-222i−2i002-2-22000000000000−2i2i−2i2i00000-22002i−2i002i−2i00-220000−2i2i−2i2i000000002i−2i00-220000000000000000
χ482-22-2222-2-222-2-2-2-222220-2-2-2-22-22-2200-22−2i2i002-2-220000000000002i−2i2i−2i00000-2200−2i2i00−2i2i00-2200002i−2i2i−2i00000000−2i2i00-220000000000000000
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χ502-22-22-12-2-22-1-211-22-12-1011-21-1-221-1−i3i32-2−2i2i00-111-100−i3i300−i3i3−i3−i3i3i3−2i2i−2i2i00000-11−i3i3i−i−33−2i2i002-20000i−ii−i00000000i−i−33-11−i3i30000000−3300000
χ512-22-22-12-2-22-1-211-22-12-1011-21-1-221-1−i3i3-222i−2i00-111-100−i3i300−i3i3−i3−i3i3i3−2i2i−2i2i000001-1i3−i3−ii3−32i−2i00-220000i−ii−i00000000−ii3−31-1i3−i30000000−3300000
χ522-22-22-12-2-22-1-211-22-12-1011-21-1-221-1−i3i3-22−2i2i00-111-100−i3i300−i3i3−i3−i3i3i32i−2i2i−2i000001-1i3−i3i−i−33−2i2i00-220000−ii−ii00000000i−i−331-1i3−i300000003−300000
χ532-22-22-12-2-22-1-211-22-12-1011-21-1-221-1i3−i32-22i−2i00-111-100i3−i300i3−i3i3i3−i3−i32i−2i2i−2i00000-11i3−i3−ii−332i−2i002-20000−ii−ii00000000−ii−33-11i3−i30000000−3300000
χ542-22-22-12-2-22-1-211-22-12-1011-21-1-221-1i3−i32-2−2i2i00-111-100i3−i300i3−i3i3i3−i3−i3−2i2i−2i2i00000-11i3−i3i−i3−3−2i2i002-20000i−ii−i00000000i−i3−3-11i3−i300000003−300000
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χ562-22-22-12-2-22-1-211-22-12-1011-21-1-221-1i3−i3-22−2i2i00-111-100i3−i300i3−i3i3i3−i3−i32i−2i2i−2i000001-1−i3i3i−i3−3−2i2i00-220000−ii−ii00000000i−i3−31-1−i3i30000000−3300000
χ572-2-22222-22-2-2-2-222-22220-22-2-2-22-22-20000002-22-22-20000000000002i−2i−2i2i0002-200000000002-20000002i−2i−2i2i00002-200000000000000000002i−2i000
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χ724444-2-244-24-2-2-2-24-21-2-2-411-2-2-2-2-2-2122-4-400001111-422222-1-1-1-1-1-100004000022-2-200000000220000000000-2000000000-1-11100000000000000
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χ844-44-44-2-22-4-2-2-42224-2-210222-112-2-1-22i3−2i300−4i4i001-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000002i−2i23−232i−2i00000000000000000000−ii−33000000000000000000
χ854-44-4-244-42442-4-4-4-2-2-240222-442-2-4-2004-40000-222-20000000000000000000004-40000000000-2200000000000000000000-220000000000000000
χ864-44-4-244-42442-4-4-4-2-2-240222-442-2-4-200-440000-222-2000000000000000000000-4400000000002-2000000000000000000002-20000000000000000
χ874-44-4-2-24-424-2222-4-21-2-20-1-122-22-221−2i32i34-400001-1-1100−2i32i300i3−i3i3i3−i3−i3000000000-22−2i32i300000000-22000000000000000000001-1i3−i300000000000000
χ884-44-4-2-24-424-2222-4-21-2-20-1-122-22-221−2i32i3-4400001-1-1100−2i32i300i3−i3i3i3−i3−i30000000002-22i3−2i3000000002-200000000000000000000-11−i3i300000000000000
χ894-44-4-2-24-424-2222-4-21-2-20-1-122-22-2212i3−2i34-400001-1-11002i3−2i300−i3i3−i3−i3i3i3000000000-222i3−2i300000000-22000000000000000000001-1−i3i300000000000000
χ904-44-4-2-24-424-2222-4-21-2-20-1-122-22-2212i3−2i3-4400001-1-11002i3−2i300−i3i3−i3−i3i3i30000000002-2−2i32i3000000002-200000000000000000000-11i3−i300000000000000
χ914-4-4444-2242-4-4-44-2-44-2-20-44222-22-2-40000004-4-22-2200000000000000000004-40000000000-2200000000000000-22000000000000000000000000
χ924-4-4444-2242-4-4-44-2-44-2-20-44222-22-2-4000000-44-22-220000000000000000000-4400000000002-2000000000000002-2000000000000000000000000
χ934-4-444-24-44-42-42-24-4-24-202-2-4224-4-2200000000-22-220000000000004i−4i−4i4i00000000000000000000000−2i2i2i−2i000000000000000000000000000000
χ944-4-444-24-44-42-42-24-4-24-202-2-4224-4-2200000000-22-22000000000000−4i4i4i−4i000000000000000000000002i−2i−2i2i000000000000000000000000000000
χ954-4-44-244-4-2-4-42-4442-2-2402-22-4-4-22420000004-4-22-220000000000000000000-2200000000004-400000000000000-22000000000000000000000000
χ964-4-44-244-4-2-4-42-4442-2-2402-22-4-4-2242000000-44-22-2200000000000000000002-20000000000-44000000000000002-2000000000000000000000000
χ974-4-44-24-22-22-42-44-22-21-202-2-1221-1-220000004-41-11-100003i−3i003i−3i3i−3i0000000-220000000000-22000000000000001-13i−3i0000000000000000000000
χ984-4-44-24-22-22-42-44-22-21-202-2-1221-1-220000004-41-11-10000−3i3i00−3i3i−3i3i0000000-220000000000-22000000000000001-1−3i3i0000000000000000000000
χ994-4-44-24-22-22-42-44-22-21-202-2-1221-1-22000000-441-11-100003i−3i003i−3i3i−3i00000002-200000000002-200000000000000-11−3i3i0000000000000000000000
χ1004-4-44-24-22-22-42-44-22-21-202-2-1221-1-22000000-441-11-10000−3i3i00−3i3i−3i3i00000002-200000000002-200000000000000-113i−3i0000000000000000000000
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
χ10388-8-88-4-4-4-8448-444-8-4-420-44-42-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-4-444-8-48-844-42-40-442-44-2-2440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4884-84-4-44-842-4-402-2-4-44444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-4444-4-444422202-222-2-2-2-2-200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4444-4-444422202-222-2-2-2-2-200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-444-484-8-84-4-42-4044-24-4-224-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-444-4-44444-42220-2-2-2-22-22-22−4i34i3000000-111-1002i3−2i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-444-4-44444-42220-2-2-2-22-22-224i3−4i3000000-111-100−2i32i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-44844-84-4-4-8-4-4204-44-2-2-4424000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-8-4-8444-4842-4-40-22444-44-4-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-44444-4-442220-22-2-2-22-22-200000000-11-1100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-44444-4-442220-22-2-2-22-22-200000000-11-110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000

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