Finite Group Databasebeta

← Group #13169368

Character table — Group #13169368

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612124444443666121212121212121212121212444121212121212121212121212121212124444121212121212121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-111111111-1-1-1-11-11-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11-1-1-1-111111111111111111111-11-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1111111-1-1-1-11111-11-1111-1-1-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-11-1-1-111-1-1111-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-111-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-1-111-1-111-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11-11-1-1-11111-1-111-1-11-1-11-1-1-1-1111111-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1111111-11-1-111-1-1-1-11111-1-111-1-111-1-1-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111-1-11-1-1-1-111-1-1111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1111111111-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-111-111111111-1-1-1
χ17222222-122-12-122-122-1-122-1-1-1-122-1-1-1-1220022-1-1-1-122-1-122-1-1-1-1-1-12020000-1-1-1-122-1-1-1-1222222-1-1-1-102020000-1-1-1-1-1-1-1-100000000-1-100000
χ18222222-122-12-122-122-1-122-1-1-1-122-1-1-1-12200-2-2-1-1-1-122-1-122-1-1-1-1-1-120-20000111122-1-1-1-1-2-2-2-2-2-21111020-20000-1-1-1-11111000000001100000
χ19222222-122-12-122-122-1-122-1-1-1-122-1-1-1-1-2-20022-1-1-1-122-1-122-1-1-1-1-1-1-2020000-1-1-1-1-2-2111122-2-2-2-211110-20200001111-1-1-1-1000000001100000
χ20222222-122-12-122-122-1-122-1-1-1-122-1-1-1-1-2-200-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-200001111-2-21111-2-22222-1-1-1-10-20-200001111111100000000-1-100000
χ21222222-122-12-122-122-1-1-22-1-1-1-122-1-111220022-1-1-1-1-2-211-2-2111111-20-20000-1-11122-1-1112222-2-211110-20-20000-1-111-1-11100000000-1-100000
χ22222222-122-12-122-122-1-1-22-1-1-1-122-1-1112200-2-2-1-1-1-1-2-211-2-2111111-202000011-1-122-1-111-2-2-2-222-1-1-1-10-2020000-1-11111-1-1000000001100000
χ23222222-122-12-122-122-1-1-22-1-1-1-122-1-111-2-20022-1-1-1-1-2-211-2-211111120-20000-1-111-2-211-1-122-2-222-1-1-1-1020-2000011-1-1-1-111000000001100000
χ24222222-122-12-122-122-1-1-22-1-1-1-122-1-111-2-200-2-2-1-1-1-1-2-211-2-2111111202000011-1-1-2-211-1-1-2-222-2-211110202000011-1-111-1-100000000-1-100000
χ2522222-122-1222-1-122-12-12-122-1-1-1-1-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-122022-1-10000-1-122220000000000-1-120-1-1-1-1-1-1-1-10000202000-1-10000-100
χ2622222-122-1222-1-122-12-12-122-1-1-1-1-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-2-2110000-1-1222200000000001-1-201111-1-1-1-10000-20-2000110000100
χ2722222-122-1222-1-122-12-12-122-1-1-1-1-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-1-22022-1-1000011-2-2-2-20000000000-1120-1-1-1-111110000-20-2000110000100
χ2822222-122-1222-1-122-12-12-122-1-1-1-1-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-211000011-2-2-2-2000000000011-20111111110000202000-1-10000-100
χ2922222-122-1222-1-122-12-1-2-122-1-1-1-1-12-2-2222200-1-1-1-11-21111-2-21111-2-2022-1-10000-1-122-2-2000000000011-20-1-111-1-1110000-202000-1-10000100
χ3022222-122-1222-1-122-12-1-2-122-1-1-1-1-12-2-222-2-200-1-1-1-11-21111-2-21111-220-2-2110000-1-122-2-20000000000-112011-1-1-1-111000020-2000110000-100
χ3122222-122-1222-1-122-12-1-2-122-1-1-1-1-12-2-2-2-22200-1-1-1-11-21111-2-211112-2022-1-1000011-2-22200000000001-1-20-1-11111-1-1000020-2000110000-100
χ3222222-122-1222-1-122-12-1-2-122-1-1-1-1-12-2-2-2-2-2-200-1-1-1-11-21111-2-21111220-2-211000011-2-2220000000000-1-12011-1-111-1-10000-202000-1-10000100
χ332222-122-122-12222-1-1-122-1-1-122-1-12-122002222-1-1-1-12-122-1-1-1-1-1-1-1-1022-1-1222222000000-1-10000000020-1-1-1-1-1-10000-1-1-1-10202-1-10000000-10
χ342222-122-122-12222-1-1-122-1-1-122-1-12-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-2-1-122-2-2-2-2000000110000000020-11-1-1-1-1000011110-20-211000000010
χ352222-122-122-12222-1-1-122-1-1-122-1-12-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-10-2211-2-22222000000-1-100000000-201-111110000-1-1-1-10-20-211000000010
χ362222-122-122-12222-1-1-122-1-1-122-1-12-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-211-2-2-2-2-2-20000001100000000-20111111000011110202-1-10000000-10
χ372222-122-122-12222-1-1-12-2-1-1-122-1-12-1-2-2002222-1-1-1-1-21-2-2111111110-2-2-1-12222-2-2000000-1-100000000-2011-1-1110000-1-111020-2-1-1000000010
χ382222-122-122-12222-1-1-12-2-1-1-122-1-12-1-2-20022-2-2-1-1-1-1-21-2-2111111110-22-1-122-2-2220000001100000000-201-1-1-111000011-1-10-202110000000-10
χ392222-122-122-12222-1-1-12-2-1-1-122-1-12-1-2-200-2-222-1-1-1-1-21-2-21111111102-211-2-222-2-2000000-1-10000000020-1111-1-10000-1-1110-202110000000-10
χ402222-122-122-12222-1-1-12-2-1-1-122-1-12-1-2-200-2-2-2-2-1-1-1-1-21-2-21111111102211-2-2-2-222000000110000000020-1-111-1-1000011-1-1020-2-1-1000000010
χ412-22-222222-2-22-2-2-2-22220-22-22-22-2-2-200002-20022-2-20000000000000002-22-2000000000000002-222-2-200002-2000000000000000000002-2000
χ422-22-222222-2-22-2-2-2-22220-22-22-22-2-2-200002-20022-2-20000000000000002-22-200000000000000-22-2-22200002-200000000000000000000-22000
χ432-22-222222-2-22-2-2-2-22220-22-22-22-2-2-20000-220022-2-2000000000000000-22-22000000000000002-222-2-20000-2200000000000000000000-22000
χ442-22-222222-2-22-2-2-2-22220-22-22-22-2-2-20000-220022-2-2000000000000000-22-2200000000000000-22-2-2220000-22000000000000000000002-2000
χ452-2-22222-2-22-2-22-2-222220-2-2-2-22-22-22002i−2i002-22-2-2200000000000000000002-2002i−2i2i−2i002-22i−2i000000000000002i−2i002-200000000002i−2i00000
χ462-2-22222-2-22-2-22-2-222220-2-2-2-22-22-22002i−2i00-222-2-220000000000000000000-22002i−2i2i−2i00-22−2i2i000000000000002i−2i00-220000000000−2i2i00000
χ472-2-22222-2-22-2-22-2-222220-2-2-2-22-22-2200−2i2i002-22-2-2200000000000000000002-200−2i2i−2i2i002-2−2i2i00000000000000−2i2i002-20000000000−2i2i00000
χ482-2-22222-2-22-2-22-2-222220-2-2-2-22-22-2200−2i2i00-222-2-220000000000000000000-2200−2i2i−2i2i00-222i−2i00000000000000−2i2i00-2200000000002i−2i00000
χ492-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1−i3i32i−2i002-2-111-100−i3i300−i3i3−i3−i3i3i30000000-11−i3i32i−2i−ii3−32-22i−2i003−33−300000000−ii3−3-11−i3i300000000−ii00000
χ502-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1−i3i32i−2i00-22-111-100−i3i300−i3i3−i3−i3i3i300000001-1i3−i32i−2i−ii3−3-22−2i2i00−33−3300000000−ii3−31-1i3−i300000000i−i00000
χ512-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1−i3i3−2i2i002-2-111-100−i3i300−i3i3−i3−i3i3i30000000-11−i3i3−2i2ii−i−332-2−2i2i00−33−3300000000i−i−33-11−i3i300000000i−i00000
χ522-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1−i3i3−2i2i00-22-111-100−i3i300−i3i3−i3−i3i3i300000001-1i3−i3−2i2ii−i−33-222i−2i003−33−300000000i−i−331-1i3−i300000000−ii00000
χ532-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1i3−i32i−2i002-2-111-100i3−i300i3−i3i3i3−i3−i30000000-11i3−i32i−2i−ii−332-22i−2i00−33−3300000000−ii−33-11i3−i300000000−ii00000
χ542-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1i3−i32i−2i00-22-111-100i3−i300i3−i3i3i3−i3−i300000001-1−i3i32i−2i−ii−33-22−2i2i003−33−300000000−ii−331-1−i3i300000000i−i00000
χ552-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1i3−i3−2i2i002-2-111-100i3−i300i3−i3i3i3−i3−i30000000-11i3−i3−2i2ii−i3−32-2−2i2i003−33−300000000i−i3−3-11i3−i300000000i−i00000
χ562-2-2222-1-2-2-1-212-2122-1-10-2111-1-221-1i3−i3−2i2i00-22-111-100i3−i300i3−i3i3i3−i3−i300000001-1−i3i3−2i2ii−i3−3-222i−2i00−33−3300000000i−i3−31-1−i3i300000000−ii00000
χ5744444-2-24-2-24-2-2-2-24-2-214-2-2-211-2-21-2-2-24400001111-2411-2-2-2-2111140000000000-2-2-2-2-2-200000000000-200000011110000000000000000000
χ5844444-2-24-2-24-2-2-2-24-2-214-2-2-211-2-21-2-2-2-4-400001111-2411-2-2-2-21111-40000000000222222000000000002000000-1-1-1-10000000000000000000
χ5944444-2-24-2-24-2-2-2-24-2-21-4-2-2-211-2-21-22244000011112-4-1-12222-1-1-1-1-40000000000-2-2-2-22200000000000200000011-1-10000000000000000000
χ6044444-2-24-2-24-2-2-2-24-2-21-4-2-2-211-2-21-222-4-4000011112-4-1-12222-1-1-1-1400000000002222-2-200000000000-2000000-1-1110000000000000000000
χ614444-24-2-24-2-2-244-2-2-21-24-211-2-2-2-2-21-2-200004411114-2-2-2-2-21111110040000-2-2-2-2000000-2-200000000000-2000000001111000000000000000
χ624444-24-2-24-2-2-244-2-2-21-24-211-2-2-2-2-21-2-20000-4-411114-2-2-2-2-211111100-4000022220000002200000000000200000000-1-1-1-1000000000000000
χ634444-24-2-24-2-2-244-2-2-21-2-4-211-2-2-2-2-21220000441111-422222-1-1-1-1-1-100-40000-2-222000000-2-20000000000020000000011-1-1000000000000000
χ644444-24-2-24-2-2-244-2-2-21-2-4-211-2-2-2-2-21220000-4-41111-422222-1-1-1-1-1-1004000022-2-20000002200000000000-200000000-1-111000000000000000
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χ854-44-4-2-24-2-2-42422-421-2-20-1-22-221-1220000-440011-1-10000−3i3i00−3i3i−3i3i0002-22-2000000000000000000000000-113i−3i00000000000000000000000
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χ894-4-444-2-2-42-2-42-2224-2-210222-112-2-1-2−2i32i3−4i4i00001-1-1100i3−i300−2i32i3i3i3−i3−i3000000000002i−2i2i−2i−2323000000000000000000−ii3−30000000000000000000
χ904-4-444-2-2-42-2-42-2224-2-210222-112-2-1-22i3−2i34i−4i00001-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000−2i2i−2i2i−2323000000000000000000i−i3−30000000000000000000
χ914-4-444-2-2-42-2-42-2224-2-210222-112-2-1-22i3−2i3−4i4i00001-1-1100−i3i3002i3−2i3−i3−i3i3i3000000000002i−2i2i−2i23−23000000000000000000−ii−330000000000000000000
χ924-4-44-2442-442-44-4-4-2-2-240222-442-2-4-20000004-4-222-200000000000000000004-400000000-2200000000000000000000-2200000000000000000
χ934-4-44-2442-442-44-4-4-2-2-240222-442-2-4-2000000-44-222-20000000000000000000-44000000002-2000000000000000000002-200000000000000000
χ944-4-44-24-22-4-2224-42-2-21-202-1-12-22-221−2i32i300004-41-1-1100−2i32i300i3−i3i3i3−i3−i30000000-22−2i32i3000000-22000000000000000000001-1i3−i3000000000000000
χ954-4-44-24-22-4-2224-42-2-21-202-1-12-22-221−2i32i30000-441-1-1100−2i32i300i3−i3i3i3−i3−i300000002-22i3−2i30000002-200000000000000000000-11−i3i3000000000000000
χ964-4-44-24-22-4-2224-42-2-21-202-1-12-22-2212i3−2i300004-41-1-11002i3−2i300−i3i3−i3−i3i3i30000000-222i3−2i3000000-22000000000000000000001-1−i3i3000000000000000
χ974-4-44-24-22-4-2224-42-2-21-202-1-12-22-2212i3−2i30000-441-1-11002i3−2i300−i3i3−i3−i3i3i300000002-2−2i32i30000002-200000000000000000000-11i3−i3000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-844844-4-4-8-4-420-44-4-2-24424000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-44-84-44-88-44-42-40-4-224444-4-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4844-8-4-84-4842-4-4024-444-2-2-44000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4444-444-4-4422202-22-2-2-2-22-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4444-444-4-4422202-22-2-2-2-22-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-48-44-8-4444-8-4-4204-442-2-44-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-4844-4-8-844-42-4042-2-44-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-4-444-444442220-22-22-22-2-2-200000000-1-11100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-4-444-444442220-22-22-22-2-2-200000000-1-1110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-484484-8-44-8-42-4-40-2444-4-224-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-444-444-42220-2-2-2-22-22-22−4i34i3000000-111-1002i3−2i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-444-444-42220-2-2-2-22-22-224i3−4i3000000-111-100−2i32i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000000

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