Finite Group Databasebeta

← Group #13168101

Character table — Group #13168101

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212244666666121212121212121212122244666666666121212121212121212121244441212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-1111111-1-1111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1-111-1-111-1-1111-11
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-111-1-1111111-1-111-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-111-1-1-1-1-1-1-111-1-1111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-111-1-11111-1-1-11-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-111-1-1111111111-111-1-1-1-111-1-1-111-1-1-111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11-1-11111-1-111-111-1-1-111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1111111111-1-11-1-11-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11-1-1111-1-111-1-1-1-111-11-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-11111111-1-111-1-11-11-111111111-1-1-1
χ17222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1222200-1-1-1-122-1-1-1-122-1-1-1-122022-1-1-1-100-1-122-1-1002222-1-1-1-12-1-1-1-1200-1-1-1-100000000-1-1000000000
χ18222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-1-22022-1-11100-1-1-2-21100-2-2-2-21111-2-1-111200-1-1110000000011000000000
χ19222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-12-20-2-211-1-1001122-1-100-2-2-2-21111211-1-1-20011-1-10000000011000000000
χ20222222-12-1222-1-1222-1-122-1-1-1-12-1-12-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-211110011-2-211002222-1-1-1-1-21111-200111100000000-1-1000000000
χ21222222-12-1222-1-1222-1-1-22-1-1-1-12-1-1211222200-1-1-1-1-2-21111-2-21111-2-2022-1-111001122-1-100-2-2221111-2-1-111-20011-1-100000000-1-1000000000
χ22222222-12-1222-1-1222-1-1-22-1-1-1-12-1-121122-2-200-1-1-1-1-2-21111-2-211112-2022-1-1-1-10011-2-2110022-2-2-1-1-1-12-1-1-1-1-20011110000000011000000000
χ23222222-12-1222-1-1222-1-1-22-1-1-1-12-1-1211-2-22200-1-1-1-1-2-21111-2-21111-220-2-2111100-1-122-1-10022-2-2-1-1-1-1-21111200-1-1-1-10000000011000000000
χ24222222-12-1222-1-1222-1-1-22-1-1-1-12-1-1211-2-2-2-200-1-1-1-1-2-21111-2-21111220-2-211-1-100-1-1-2-21100-2-2221111211-1-1200-1-11100000000-1-1000000000
χ2522222-1222-12-122-12-12-12-12-12-1-12-1-122002222-1-1-1-1-1222-1-1-1-1-1-1-1-1202000022-1-100-1-1222200000000-100-1-102-100-1-1-1-1-1-1002200-1-10000-100
χ2622222-1222-12-122-12-12-12-12-12-1-12-1-1220022-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-120-20000221100-1-122-2-200000000-100-1-10-2100-1-1111100-2-200110000100
χ2722222-1222-12-122-12-12-12-12-12-1-12-1-12200-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-1-2020000-2-2-1-10011-2-222000000001001102-10011-1-1-1-100-2-200110000100
χ2822222-1222-12-122-12-12-12-12-12-1-12-1-12200-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-20-20000-2-2110011-2-2-2-200000000100110-2100111111002200-1-10000-100
χ2922222-1222-12-122-12-12-1-2-12-12-1-12-1-1-2-2002222-1-1-1-11-2-2-211111111-20-20000-2-2-1-100-1-1222200000000100110-2100-1-111-1-1002-200-1-10000100
χ3022222-1222-12-122-12-12-1-2-12-12-1-12-1-1-2-20022-2-2-1-1-1-11-2-2-211111111-2020000-2-21100-1-122-2-2000000001001102-100-1-1-1-11100-2200110000-100
χ3122222-1222-12-122-12-12-1-2-12-12-1-12-1-1-2-200-2-222-1-1-1-11-2-2-21111111120-2000022-1-10011-2-22200000000-100-1-10-21001111-1-100-2200110000-100
χ3222222-1222-12-122-12-12-1-2-12-12-1-12-1-1-2-200-2-2-2-2-1-1-1-11-2-2-211111111202000022110011-2-2-2-200000000-100-1-102-10011-1-111002-200-1-10000100
χ332222-122-122-12222-1-1-122-1-12-12-1-12-122220022-1-1-1-12-1-1-122-1-1-1-1-1-1022-1-1220022220000-1-1000000000-1-100-1-12-1-100-1-1-1-122000000-1-1000-10
χ342222-122-122-12222-1-1-122-1-12-12-1-12-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-102-2-1-12200-2-222000011000000000-1-100-11-2-1-1001111-2-20000001100010
χ352222-122-122-12222-1-1-122-1-12-12-1-12-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-10-2211-2-20022-2-20000-1-100000000011001-121100-1-1-1-1-2-20000001100010
χ362222-122-122-12222-1-1-122-1-12-12-1-12-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-211-2-200-2-2-2-2000011000000000110011-21100111122000000-1-1000-10
χ372222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-2220022-1-1-1-1-2111-2-21111110-2-2-1-1220022-2-20000-1-1000000000-1-10011-2110011-1-12-2000000-1-100010
χ382222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-22200-2-2-1-1-1-1-2111-2-21111110-22-1-12200-2-2-2-2000011000000000-1-1001-121100-1-111-2200000011000-10
χ392222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-2-2-20022-1-1-1-1-2111-2-211111102-211-2-20022220000-1-10000000001100-11-2-1-10011-1-1-2200000011000-10
χ402222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-2-2-200-2-2-1-1-1-1-2111-2-211111102211-2-200-2-2220000110000000001100-1-12-1-100-1-1112-2000000-1-100010
χ4122-2-2222-2-2-2222-2-2-22220-2-2-2-2-2222-20000002i−2i22-2-20000000000000000000002i−2i0000002i−2i2-20022-2-2000000000000002i−2i00000000002i−2i000
χ4222-2-2222-2-2-2222-2-2-22220-2-2-2-2-2222-20000002i−2i22-2-20000000000000000000002i−2i0000002i−2i-2200-2-222000000000000002i−2i0000000000−2i2i000
χ4322-2-2222-2-2-2222-2-2-22220-2-2-2-2-2222-2000000−2i2i22-2-2000000000000000000000−2i2i000000−2i2i2-20022-2-200000000000000−2i2i0000000000−2i2i000
χ4422-2-2222-2-2-2222-2-2-22220-2-2-2-2-2222-2000000−2i2i22-2-2000000000000000000000−2i2i000000−2i2i-2200-2-22200000000000000−2i2i00000000002i−2i000
χ452-2-2222222-2-2-2-2-22-22220222-2-2-2-2-2-2002-22i−2i002-22-20000000000000002-22-20000002i−2i2i−2i00002i−2i000002-200000002i−2i000000002i−2i000000000
χ462-2-2222222-2-2-2-2-22-22220222-2-2-2-2-2-2002-2−2i2i002-22-20000000000000002-22-2000000−2i2i−2i2i0000−2i2i000002-20000000−2i2i00000000−2i2i000000000
χ472-2-2222222-2-2-2-2-22-22220222-2-2-2-2-2-200-222i−2i002-22-2000000000000000-22-220000002i−2i2i−2i0000−2i2i00000-2200000002i−2i00000000−2i2i000000000
χ482-2-2222222-2-2-2-2-22-22220222-2-2-2-2-2-200-22−2i2i002-22-2000000000000000-22-22000000−2i2i−2i2i00002i−2i00000-220000000−2i2i000000002i−2i000000000
χ492-2-2222-12-1-2-2-2112-22-1-102-1-111-211-23−32-22i−2i00-11-11003−33−30033−3−30002-2-11−i3i3003−32i−2i−ii00002i−2i−i3i3−i3i30-11−i3i30003−3−ii00000000−ii000000000
χ502-2-2222-12-1-2-2-2112-22-1-102-1-111-211-23−32-2−2i2i00-11-11003−33−30033−3−30002-2-11i3−i3003−3−2i2ii−i0000−2i2ii3−i3i3−i30-11i3−i30003−3i−i00000000i−i000000000
χ512-2-2222-12-1-2-2-2112-22-1-102-1-111-211-23−3-222i−2i00-11-11003−33−30033−3−3000-221-1−i3i300−332i−2i−ii0000−2i2ii3−i3i3−i301-1−i3i3000−33−ii00000000i−i000000000
χ522-2-2222-12-1-2-2-2112-22-1-102-1-111-211-23−3-22−2i2i00-11-11003−33−30033−3−3000-221-1i3−i300−33−2i2ii−i00002i−2i−i3i3−i3i301-1i3−i3000−33i−i00000000−ii000000000
χ532-2-2222-12-1-2-2-2112-22-1-102-1-111-211-2−332-22i−2i00-11-1100−33−3300−3−3330002-2-11i3−i300−332i−2i−ii00002i−2ii3−i3i3−i30-11i3−i3000−33−ii00000000−ii000000000
χ542-2-2222-12-1-2-2-2112-22-1-102-1-111-211-2−332-2−2i2i00-11-1100−33−3300−3−3330002-2-11−i3i300−33−2i2ii−i0000−2i2i−i3i3−i3i30-11−i3i3000−33i−i00000000i−i000000000
χ552-2-2222-12-1-2-2-2112-22-1-102-1-111-211-2−33-222i−2i00-11-1100−33−3300−3−333000-221-1i3−i3003−32i−2i−ii0000−2i2i−i3i3−i3i301-1i3−i30003−3−ii00000000i−i000000000
χ562-2-2222-12-1-2-2-2112-22-1-102-1-111-211-2−33-22−2i2i00-11-1100−33−3300−3−333000-221-1−i3i3003−3−2i2ii−i00002i−2ii3−i3i3−i301-1−i3i30003−3i−i00000000−ii000000000
χ5744444-2-24-2-24-2-2-2-24-2-214-2-21-21-2-21-2-2-20044001111-24-2-211-2-211114000000-2-20000-2-2-2-20000000000-2001100000110000000000000000000
χ5844444-2-24-2-24-2-2-2-24-2-214-2-21-21-2-21-2-2-200-4-4001111-24-2-211-2-21111-400000022000022220000000000200-1-100000-1-10000000000000000000
χ5944444-2-24-2-24-2-2-2-24-2-21-4-2-21-21-2-21-22200440011112-422-1-122-1-1-1-1-4000000220000-2-2-2-20000000000200-1-100000110000000000000000000
χ6044444-2-24-2-24-2-2-2-24-2-21-4-2-21-21-2-21-22200-4-40011112-422-1-122-1-1-1-14000000-2-2000022220000000000-2001100000-1-10000000000000000000
χ614444-24-2-2-24-24-2-24-2-21-24-21-21-2-21-2-2-2-244000011114-211-2-2-2-21111040-2-2-2-20000-2-20000000000000001100-20011000000000000000000000
χ624444-24-2-2-24-24-2-24-2-21-24-21-21-2-21-2-2-2-2-4-4000011114-211-2-2-2-211110-402222000022000000000000000-1-100200-1-1000000000000000000000
χ634444-24-2-2-24-24-2-24-2-21-2-4-21-21-2-21-2-2224400001111-42-1-12222-1-1-1-10-40-2-2-2-20000220000000000000001100200-1-1000000000000000000000
χ644444-24-2-2-24-24-2-24-2-21-2-4-21-21-2-21-2-222-4-400001111-42-1-12222-1-1-1-104022220000-2-2000000000000000-1-100-20011000000000000000000000
χ654444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-2-21440000441111-2-2-2-2-2-2111111004000000-2-2000000-2-200000000000000-2-200001111000000000000000
χ664444-2-24-24-2-2-244-2-21-2-241-2-2-2-21-2-21440000-4-41111-2-2-2-2-2-211111100-4000000220000002200000000000000220000-1-1-1-1000000000000000
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χ684444-2-24-24-2-2-244-2-21-2-2-41-2-2-2-21-2-21-4-40000-4-41111222222-1-1-1-1-1-1004000000220000002200000000000000-2-2000011-1-1000000000000000
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χ794-44-4444-4-44-4-4-44-444440-4-4-444-4-4-44000000004-4-440000000000000000000000000000000000000000000000000000000000000000000000
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χ884-4-444-2-24-22-4222-2-4-2-210-2-212-122-1223−23004i−4i001-11-10023−23−3300−3−3330000000−2i32i30000−2i2i−2i2i0000000000000i3−i300000i−i0000000000000000000
χ894-4-444-2-24-22-4222-2-4-2-210-2-212-122-1223−2300−4i4i001-11-10023−23−3300−3−33300000002i3−2i300002i−2i2i−2i0000000000000−i3i300000−ii0000000000000000000
χ904-4-444-2-24-22-4222-2-4-2-210-2-212-122-12−2323004i−4i001-11-100−23233−30033−3−300000002i3−2i30000−2i2i−2i2i0000000000000−i3i300000i−i0000000000000000000
χ914-4-444-2-24-22-4222-2-4-2-210-2-212-122-12−232300−4i4i001-11-100−23233−30033−3−30000000−2i32i300002i−2i2i−2i0000000000000i3−i300000−ii0000000000000000000
χ924-4-44-244-24-42-4-4-442-2-240-2-242-422-42004-40000-22-22000000000000000-224-4000000000000000000000-220000000000000000000000000000
χ934-4-44-244-24-42-4-4-442-2-240-2-242-422-4200-440000-22-220000000000000002-2-440000000000000000000002-20000000000000000000000000000
χ944-4-44-24-2-2-2-42-42242-21-20-21-2-122-12223−234-400001-11-100−3323−2300−3−333000-22-22000023−230000000000000001-100000−33000000000000000000000
χ954-4-44-24-2-2-2-42-42242-21-20-21-2-122-12223−23-4400001-11-100−3323−2300−3−3330002-22-20000−2323000000000000000-11000003−3000000000000000000000
χ964-4-44-24-2-2-2-42-42242-21-20-21-2-122-122−23234-400001-11-1003−3−23230033−3−3000-22-220000−23230000000000000001-1000003−3000000000000000000000
χ974-4-44-24-2-2-2-42-42242-21-20-21-2-122-122−2323-4400001-11-1003−3−23230033−3−30002-22-2000023−23000000000000000-1100000−33000000000000000000000
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
χ10088-8-88-4-4-8448-4-444-8-4-42044-24-2-4-4240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-444-8-48-44-84-42-404-24-24-42-440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4444-4-4-44442220-2-2-2-2-2222-200000000-1-1110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4444-4-4-44442220-2-2-2-2-2222-200000000-1-111000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-84-4-844-448-4-42044-2-4244-2-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-44484-84-4-8-4-42-404-242-44-24-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-484-8-444-884-42-4-40-244-4-4-2442000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-4444-44-42220-2-2-222-2-2-2200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-444-4444-44-42220-2-2-222-2-2-2200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-48444-8-8-442-4-402-4-444-244-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4-444444-442220222-2-2-2-2-2-243−43000000-11-1100−2323−23230033−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4-444444-442220222-2-2-2-2-2-2−4343000000-11-110023−2323−2300−3−3330000000000000000000000000000000000000000000000000000000000

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