Finite Group Databasebeta

← Group #13168330

Character table — Group #13168330

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666633346666666661212224436661212121212121212121212124444666612121212121212121212121244444444121212126612121212121212121212121212122412121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111111-1-11111-1-111-1-111-1-1111111-111-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111-11111-1-1-1-11111-11-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-111-1-1-1-1-1-1-1-11-1-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1111111111-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-1-1-11111-1-1-111111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1111-111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-11-11-1-111-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-11111-1-11-11-111-1-111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-11-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-111-111111-1-1-11-11
χ17222222-122-1-1222-12-1-122-1-12-12-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10222000022-1-1-1-100222200000022000000-1-10200-1-1-1-1-1-1-1-12000-1-100-1000
χ18222222-122-1-1222-12-1-122-1-12-12-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-22000022-1-1110022-2-2000000-2-20000001-10-200-1-1-1-11111-200011001000
χ19222222-122-1-1222-12-1-122-1-12-12-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1022-20000-2-211-1-100-2-222000000-2-2000000-1102001111-1-1-1-1-200011001000
χ20222222-122-1-1222-12-1-122-1-12-12-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-20000-2-2111100-2-2-2-200000022000000110-200111111112000-1-100-1000
χ21222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-20022-1-1-1-11-2-2-21111111102-2-2000022-1-1-1-100-2-2-2-20000002200000011020011-1-1-1-111-2000-1-1001000
χ22222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-20022-1-1-1-11-2-2-2111111110-22-2000022-1-11100-2-222000000-2-2000000-110-20011-1-111-1-120001100-1000
χ23222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-200-2-2-1-1-1-11-2-2-21111111102-220000-2-211-1-10022-2-2000000-2-20000001-10200-1-111-1-11120001100-1000
χ24222222-122-1-1222-12-1-12-2-1-12-12-12-1-1-2-200-2-2-1-1-1-11-2-2-2111111110-2220000-2-2111100222200000022000000-1-10-200-1-11111-1-1-2000-1-1001000
χ2522222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-12222-1-1-1-122-1-122-1-1-1-1-1-1200222-1-1-1-12200-1-1-1-10022002200-1-1-1-1-1-10220-1-1-1-1-1-1000000-1-100000000
χ2622222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1200-222-1-111-2-200-1-11100-2-200-2-2001111-1-10-220-1-111110000001100000000
χ2722222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-2002-2-211-1-1220011-1-100-2-200-2-20011111102-2011-1-1-1-10000001100000000
χ2822222-122-1222-1-1222-1-122-1-12-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-200-2-2-21111-2-20011110022002200-1-1-1-1110-2-20111111000000-1-100000000
χ2922222-122-1222-1-1222-1-1-22-1-12-1-1-1-12112222-1-1-1-1-2-211-2-2111111-200-222-1-1-1-122001111002200-2-2001111-1-10-2-201111-1-1000000-1-100000000
χ3022222-122-1222-1-1222-1-1-22-1-12-1-1-1-121122-2-2-1-1-1-1-2-211-2-2111111-200222-1-111-2-20011-1-100-2-2002200-1-1-1-1-1-102-2011-1-1110000001100000000
χ3122222-122-1222-1-1222-1-1-22-1-12-1-1-1-1211-2-222-1-1-1-1-2-211-2-2111111200-2-2-211-1-12200-1-11100-2-2002200-1-1-1-1110-220-1-111-1-10000001100000000
χ3222222-122-1222-1-1222-1-1-22-1-12-1-1-1-1211-2-2-2-2-1-1-1-1-2-211-2-21111112002-2-21111-2-200-1-1-1-1002200-2-2001111110220-1-1-1-111000000-1-100000000
χ332222-122-1222-1222-1-12-12-12-1-1-12-12-1222200-1-1-1-12-1-1-1-1-122-1-1-1-12220-1-1220000222200-1-1002200000000-1-120-1-1-1-10000-1-1-1-1020000-1-10-100
χ342222-122-1222-1222-1-12-12-12-1-1-12-12-1222200-1-1-1-12-1-1-1-1-122-1-1-1-12-2-20-1-1220000-2-222001100-2-200000000-1-1-20-11-1-1000011110-20000110100
χ352222-122-1222-1222-1-12-12-12-1-1-12-12-122-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-222011-2-2000022-2-200-1-100-2-20000000011201-1110000-1-1-1-10-20000110100
χ362222-122-1222-1222-1-12-12-12-1-1-12-12-122-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2011-2-20000-2-2-2-2001100220000000011-20111100001111020000-1-10-100
χ372222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-22200-1-1-1-1-211111-2-21111-22-20-1-122000022-2-2001100-2-200000000-1-1-201-1110000-1-111020000110-100
χ382222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-22200-1-1-1-1-211111-2-21111-2-220-1-1220000-2-2-2-200-1-1002200000000-1-1201111000011-1-10-20000-1-10100
χ392222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-2-2-200-1-1-1-1-211111-2-2111122-2011-2-200002222001100220000000011-20-1-1-1-10000-1-1110-20000-1-10100
χ402222-122-1222-1222-1-12-1-2-12-1-1-12-12-1-2-2-2-200-1-1-1-1-211111-2-211112-22011-2-20000-2-22200-1-100-2-2000000001120-11-1-1000011-1-1020000110-100
χ412-22-2222-2-2-22-22-2-222220-22-2-2-2-22-2200000022-2-200000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i000000000000000000002i−2i2-20000
χ422-22-2222-2-2-22-22-2-222220-22-2-2-2-22-2200000022-2-200000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i00000000000000000000−2i2i2-20000
χ432-22-2222-2-2-22-22-2-222220-22-2-2-2-22-2200000022-2-20000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i00000000000000000000−2i2i-220000
χ442-22-2222-2-2-22-22-2-222220-22-2-2-2-22-2200000022-2-20000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i000000000000000000002i−2i-220000
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χ472-2-222222-2-2-2-2-222-222202-22-2-22-2-2-200-222i−2i2-22-20000000000000000-22-222i−2i2i−2i00000000−2i2i0000000000-22000000002i−2i000000−2i2i00000000
χ482-2-222222-2-2-2-2-222-222202-22-2-22-2-2-200-22−2i2i2-22-20000000000000000-22-22−2i2i−2i2i000000002i−2i0000000000-2200000000−2i2i0000002i−2i00000000
χ492-2-222-1221-2-2-21-12-22-1-1021-1-21-111-23−32-22i−2i-11-11003−3003−333−3−300002-2-11−ii2i−2i003−3−i3i3002i−2i000000−i3i3−i3i3-1100003−3−i3i3−ii000000−ii00000000
χ502-2-222-1221-2-2-21-12-22-1-1021-1-21-111-23−32-2−2i2i-11-11003−3003−333−3−300002-2-11i−i−2i2i003−3i3−i300−2i2i000000i3−i3i3−i3-1100003−3i3−i3i−i000000i−i00000000
χ512-2-222-1221-2-2-21-12-22-1-1021-1-21-111-23−3-222i−2i-11-11003−3003−333−3−30000-221-1−ii2i−2i00−33−i3i300−2i2i000000i3−i3i3−i31-10000−33−i3i3−ii000000i−i00000000
χ522-2-222-1221-2-2-21-12-22-1-1021-1-21-111-23−3-22−2i2i-11-11003−3003−333−3−30000-221-1i−i−2i2i00−33i3−i3002i−2i000000−i3i3−i3i31-10000−33i3−i3i−i000000−ii00000000
χ532-2-222-1221-2-2-21-12-22-1-1021-1-21-111-2−332-22i−2i-11-1100−3300−33−3−33300002-2-11−ii2i−2i00−33i3−i3002i−2i000000i3−i3i3−i3-110000−33i3−i3−ii000000−ii00000000
χ542-2-222-1221-2-2-21-12-22-1-1021-1-21-111-2−332-2−2i2i-11-1100−3300−33−3−33300002-2-11i−i−2i2i00−33−i3i300−2i2i000000−i3i3−i3i3-110000−33−i3i3i−i000000i−i00000000
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χ634444-24-2-24-2-2-244-2-21-2-2-41-2-21-2-2-2-21-4-4000011112222-1-122-1-1-1-104-4000000000-2-200002200000000000000200-200000011-1-1000000000000
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χ904-4-444-2-24222-42-2-2-4-21-20-2-1-22212-12−2323004i−4i1-11-100−2323003−333−3−300000000−2i2i−2i2i00002i3−2i30000000000000000000000−i3i3i−i0000000000000000
χ914-4-444-2-24222-42-2-2-4-21-20-2-1-22212-12−232300−4i4i1-11-100−2323003−333−3−3000000002i−2i2i−2i0000−2i32i30000000000000000000000i3−i3−ii0000000000000000
χ924-4-44-244-2-4-4-42-4442-24-20-2-4-22242-42004-400-22-220000000000000000-224-4000000000000000000000000-2200000000000000000000000000
χ934-4-44-244-2-4-4-42-4442-24-20-2-4-22242-4200-4400-22-2200000000000000002-2-440000000000000000000000002-200000000000000000000000000
χ944-4-44-2-24-22-4-422-242-2-210-2212-1-2-12223−234-4001-11-100−330023−23−3−3330000-22-2200000023−2300000000000000001-10000−3300000000000000000000
χ954-4-44-2-24-22-4-422-242-2-210-2212-1-2-12223−23-44001-11-100−330023−23−3−33300002-22-2000000−23230000000000000000-1100003−300000000000000000000
χ964-4-44-2-24-22-4-422-242-2-210-2212-1-2-122−23234-4001-11-1003−300−232333−3−30000-22-22000000−232300000000000000001-100003−300000000000000000000
χ974-4-44-2-24-22-4-422-242-2-210-2212-1-2-122−2323-44001-11-1003−300−232333−3−300002-22-200000023−230000000000000000-110000−3300000000000000000000
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
χ10088-8-88-4-4-8-4-448444-8-42-404-24-4-4-24240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-484-48-8-444-84-4-42044-2-424-2-440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-4-44-444442220-2-2-222-2-22-2000000-111-100006-600-33-33000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-4-44-444442220-2-2-222-2-22-2000000-111-10000-66003-33-3000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-844-4-8-4448-42-4042444-2-4-2-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-44-84-448-84-42-4-40-2-44-244-44200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4844-884-44-8-4-4-4204-4-24-2424-400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4444-44-444-42220-22-2-2-2-22-22000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4444-44-444-42220-22-2-2-2-22-22000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-4-8444-88-442-4-4024-4-24-444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444444-4-4422202-22-2-22-2-2-243−430000-11-1100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444444-4-4422202-22-2-22-2-2-2−43430000-11-110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000000

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