Finite Group Databasebeta

← Group #13168588

Character table — Group #13168588

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666663334666666666121244444436661212121212121212121212122226666121212121212121212121212444412121212666666666612121212121244441212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-111111111111111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-11111-1-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-111-1-11111-11-1-1-1-111-1-111-1-1111-1-11-1-111-1-111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-11111-1111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-11111-1-111111-1-1-111-1-1-1-1-1-11111-111-1-1-1-1-111111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-1-1-11111-1-111111-11111-1-111-1-111-1-11-1-11-1-111-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-11-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11-11-111111111-1-1-1
χ17222222-1222-1-1222-12-1-122-1-12-1-12-1-122002222-1-1-1-12-122-1-1-1-1-1-1-1-1022002200-1-122-1-10022000000000-12-100-1-1-1-100-1-1-1-100220000-1-1000-10
χ18222222-1222-1-1222-12-1-122-1-12-1-12-1-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-2002200-1-1-2-2110022000000000-1-2100-1-11100-1-11100-2-200001100010
χ19222222-1222-1-1222-12-1-122-1-12-1-12-1-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-10-2200-2-2001122-1-100-2-200000000012-10011-1-10011-1-100-2-200001100010
χ20222222-1222-1-1222-12-1-122-1-12-1-12-1-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-200-2-20011-2-21100-2-20000000001-2100111100111100220000-1-1000-10
χ21222222-1222-1-1222-12-1-1-22-1-12-1-12-1-1-2-2002222-1-1-1-1-21-2-2111111110-2-200-2-200-1-122-1-100220000000001-2100111100-1-1-1-1002-20000-1-100010
χ22222222-1222-1-1222-12-1-1-22-1-12-1-12-1-1-2-20022-2-2-1-1-1-1-21-2-2111111110-2200-2-200-1-1-2-211002200000000012-10011-1-100-1-11100-22000011000-10
χ23222222-1222-1-1222-12-1-1-22-1-12-1-12-1-1-2-200-2-222-1-1-1-1-21-2-21111111102-20022001122-1-100-2-2000000000-1-2100-1-1110011-1-100-22000011000-10
χ24222222-1222-1-1222-12-1-1-22-1-12-1-12-1-1-2-200-2-2-2-2-1-1-1-1-21-2-21111111102200220011-2-21100-2-2000000000-12-100-1-1-1-1001111002-20000-1-100010
χ2522222-122-1-12222-12-12-12-12-1-12-1-12-122220022-1-1-1-1-12-1-122-1-1-1-1-1-12022200-1-100-1-122220000000000-10-12-1-100-1-1-1-100-1-1220000-1-10000-100
χ2622222-122-1-12222-12-12-12-12-1-12-1-12-1222200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-120-22200-1-10011-2-2220000000000-101-2-1-10011-1-10011-2-20000110000100
χ2722222-122-1-12222-12-12-12-12-1-12-1-12-122-2-20022-1-1-1-1-12-1-122-1-1-1-1-1-1-202-2-2001100-1-122-2-2000000000010-121100-1-11100-1-1-2-20000110000100
χ2822222-122-1-12222-12-12-12-12-1-12-1-12-122-2-200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-2-200110011-2-2-2-20000000000101-2110011110011220000-1-10000-100
χ2922222-122-1-12222-12-12-1-2-12-1-12-1-12-1-2-2220022-1-1-1-11-211-2-2111111-20-2-2-200-1-100-1-122220000000000101-2110011-1-100-1-12-20000-1-10000100
χ3022222-122-1-12222-12-12-1-2-12-1-12-1-12-1-2-22200-2-2-1-1-1-11-211-2-2111111-202-2-200-1-10011-2-222000000000010-121100-1-1-1-10011-220000110000-100
χ3122222-122-1-12222-12-12-1-2-12-1-12-1-12-1-2-2-2-20022-1-1-1-11-211-2-211111120-222001100-1-122-2-20000000000-101-2-1-100111100-1-1-220000110000-100
χ3222222-122-1-12222-12-12-1-2-12-1-12-1-12-1-2-2-2-200-2-2-1-1-1-11-211-2-21111112022200110011-2-2-2-20000000000-10-12-1-100-1-11100112-20000-1-10000100
χ332222-122-12222-1-122-1-122-1-12-1-12-1-12-1-1222200-1-1-1-122-1-1-1-122-1-1-1-1220-1-1-1-122220000-1-1-1-12222-1-1-1-12200-1-1-1-100-1-1-1-1000000-1-1000000000
χ342222-122-12222-1-122-1-122-1-12-1-12-1-12-1-122-2-200-1-1-1-122-1-1-1-122-1-1-1-12-20-1-11122-2-20000-1-111-2-2-2-211112-200-1-11100-1-11100000011000000000
χ352222-122-12222-1-122-1-122-1-12-1-12-1-12-1-1-2-22200-1-1-1-122-1-1-1-122-1-1-1-1-22011-1-1-2-222000011-1-1-2-2-2-21111-220011-1-10011-1-100000011000000000
χ362222-122-12222-1-122-1-122-1-12-1-12-1-12-1-1-2-2-2-200-1-1-1-122-1-1-1-122-1-1-1-1-2-201111-2-2-2-2000011112222-1-1-1-1-2-2001111001111000000-1-1000000000
χ372222-122-12222-1-122-1-12-2-1-12-1-12-1-1211222200-1-1-1-1-2-21111-2-21111-2-20111122220000-1-1-1-1-2-2221111-2-200111100-1-1-1-1000000-1-1000000000
χ382222-122-12222-1-122-1-12-2-1-12-1-12-1-121122-2-200-1-1-1-1-2-21111-2-21111-22011-1-122-2-20000-1-11122-2-2-1-1-1-1-220011-1-100-1-11100000011000000000
χ392222-122-12222-1-122-1-12-2-1-12-1-12-1-1211-2-22200-1-1-1-1-2-21111-2-211112-20-1-111-2-222000011-1-122-2-2-1-1-1-12-200-1-1110011-1-100000011000000000
χ402222-122-12222-1-122-1-12-2-1-12-1-12-1-1211-2-2-2-200-1-1-1-1-2-21111-2-21111220-1-1-1-1-2-2-2-200001111-2-22211112200-1-1-1-1001111000000-1-1000000000
χ4122-2-2222-22-22-2-22-2-22220-2-22-2-2-222-20000002i−2i22-2-2000000000000000000000002i−2i2i−2i00002-20022-2-2000000000000002i−2i00000000002i−2i000
χ4222-2-2222-22-22-2-22-2-22220-2-22-2-2-222-20000002i−2i22-2-2000000000000000000000002i−2i2i−2i0000-2200-2-222000000000000002i−2i0000000000−2i2i000
χ4322-2-2222-22-22-2-22-2-22220-2-22-2-2-222-2000000−2i2i22-2-200000000000000000000000−2i2i−2i2i00002-20022-2-200000000000000−2i2i0000000000−2i2i000
χ4422-2-2222-22-22-2-22-2-22220-2-22-2-2-222-2000000−2i2i22-2-200000000000000000000000−2i2i−2i2i0000-2200-2-22200000000000000−2i2i00000000002i−2i000
χ452-2-22222-2-22-222-2-2-2222022-2-2-2-2-2-22002i−2i2i−2i002-22-200000000000000000002i−2i2i−2i00002i−2i2i−2i002-2000000000000002i−2i2i−2i0000002-2000000000
χ462-2-22222-2-22-222-2-2-2222022-2-2-2-2-2-22002i−2i−2i2i002-22-200000000000000000002i−2i−2i2i00002i−2i−2i2i00-22000000000000002i−2i−2i2i000000-22000000000
χ472-2-22222-2-22-222-2-2-2222022-2-2-2-2-2-2200−2i2i2i−2i002-22-20000000000000000000−2i2i2i−2i0000−2i2i2i−2i00-2200000000000000−2i2i2i−2i000000-22000000000
χ482-2-22222-2-22-222-2-2-2222022-2-2-2-2-2-2200−2i2i−2i2i002-22-20000000000000000000−2i2i−2i2i0000−2i2i−2i2i002-200000000000000−2i2i−2i2i0000002-2000000000
χ492-2-22-1221-22-22-11-2-2-1-120-1-1-211-21123−32i−2i2i−2i00-11-11003−33−30033−3−3000−i3i3−i3i32i−2i2i−2i0000−ii−ii002-23−33−30000−i3i3−i3i300−ii−ii000000-11000000000
χ502-2-22-1221-22-22-11-2-2-1-120-1-1-211-21123−32i−2i−2i2i00-11-11003−33−30033−3−3000−i3i3i3−i32i−2i−2i2i0000−iii−i00-22−33−330000−i3i3i3−i300−iii−i0000001-1000000000
χ512-2-22-1221-22-22-11-2-2-1-120-1-1-211-21123−3−2i2i2i−2i00-11-11003−33−30033−3−3000i3−i3−i3i3−2i2i2i−2i0000i−i−ii00-22−33−330000i3−i3−i3i300i−i−ii0000001-1000000000
χ522-2-22-1221-22-22-11-2-2-1-120-1-1-211-21123−3−2i2i−2i2i00-11-11003−33−30033−3−3000i3−i3i3−i3−2i2i−2i2i0000i−ii−i002-23−33−30000i3−i3i3−i300i−ii−i000000-11000000000
χ532-2-22-1221-22-22-11-2-2-1-120-1-1-211-2112−332i−2i2i−2i00-11-1100−33−3300−3−333000i3−i3i3−i32i−2i2i−2i0000−ii−ii002-2−33−330000i3−i3i3−i300−ii−ii000000-11000000000
χ542-2-22-1221-22-22-11-2-2-1-120-1-1-211-2112−332i−2i−2i2i00-11-1100−33−3300−3−333000i3−i3−i3i32i−2i−2i2i0000−iii−i00-223−33−30000i3−i3−i3i300−iii−i0000001-1000000000
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χ5744444-2-24-2-2-2-244-2-2-2-214-2-21-2-21-2-21440000441111-2-2-2-2-2-211111100400000000-2-2-2-200000000000000-2-2000011000011000000000000000
χ5844444-2-24-2-2-2-244-2-2-2-214-2-21-2-21-2-21440000-4-41111-2-2-2-2-2-211111100-400000000222200000000000000220000-1-10000-1-1000000000000000
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χ6044444-2-24-2-2-2-244-2-2-2-21-4-2-21-2-21-2-21-4-40000-4-41111222222-1-1-1-1-1-100400000000222200000000000000-2-20000110000-1-1000000000000000
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χ624444-24-2-244-2-2-2-24-2-21-24-21-2-21-2-21-2-2-200-4-40011114-2-2-211-2-211110-40002200220000002200000000020000-1-10000-1-100000000000000000
χ634444-24-2-244-2-2-2-24-2-21-2-4-21-2-21-2-21-2220044001111-4222-1-122-1-1-1-10-40002200-2-2000000-2-200000000020000-1-100001100000000000000000
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χ884-4-444-24-42-2-444-42-4-24-20-2422-422-4-2004i−4i0000-22-220000000000000000000−2i2i0000004i−4i00000000000000000000−2i2i0000000000000000000
χ894-4-444-24-42-2-444-42-4-24-20-2422-422-4-200−4i4i0000-22-2200000000000000000002i−2i000000−4i4i000000000000000000002i−2i0000000000000000000
χ904-4-44-24-22-442-2-22-42-21-20-2122-122-1-223−23004i−4i001-11-10023−23−3300−3−33300000−2i32i300−2i2i000000−2i2i00000000000000i3−i30000i−i00000000000000000
χ914-4-44-24-22-442-2-22-42-21-20-2122-122-1-223−2300−4i4i001-11-10023−23−3300−3−333000002i3−2i3002i−2i0000002i−2i00000000000000−i3i30000−ii00000000000000000
χ924-4-44-24-22-442-2-22-42-21-20-2122-122-1-2−2323004i−4i001-11-100−23233−30033−3−3000002i3−2i300−2i2i000000−2i2i00000000000000−i3i30000i−i00000000000000000
χ934-4-44-24-22-442-2-22-42-21-20-2122-122-1-2−232300−4i4i001-11-100−23233−30033−3−300000−2i32i3002i−2i0000002i−2i00000000000000i3−i30000−ii00000000000000000
χ944-4-44-2-2422-2-44-222-41-2-201-22-122-12-223−234i−4i00001-11-100−3323−2300−3−333000−2i32i300−2i2i000000−2i2i00000000000000i3−i30000i−i0000000000000000000
χ954-4-44-2-2422-2-44-222-41-2-201-22-122-12-223−23−4i4i00001-11-100−3323−2300−3−3330002i3−2i3002i−2i0000002i−2i00000000000000−i3i30000−ii0000000000000000000
χ964-4-44-2-2422-2-44-222-41-2-201-22-122-12-2−23234i−4i00001-11-1003−3−23230033−3−30002i3−2i300−2i2i000000−2i2i00000000000000−i3i30000i−i0000000000000000000
χ974-4-44-2-2422-2-44-222-41-2-201-22-122-12-2−2323−4i4i00001-11-1003−3−23230033−3−3000−2i32i3002i−2i0000002i−2i00000000000000i3−i30000−ii0000000000000000000
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
χ10088-8-8-48-448-8-444-4-84-42-404-2-44-24-4240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-484-448-84-44-82-4-40-24-4-2442-440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-44-444-4442220-2-22-2-2-222-200000000-1-1110000006i−6i−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-44-444-4442220-2-22-2-2-222-200000000-1-111000000−6i6i3i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-484444-8-8-4-4-4-42044-2-4-4244-2000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4-4-8-844448-4-42-404-24-42-44-24000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48-444-8-844-482-4-40-2442-4-4-244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-4444444-4-42220-2-2-2222-2-2-200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-4444444-4-42220-2-2-2222-2-2-200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1098-8-888-4-4-84-44-48-844-4-420-4-4-244-2442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-44-4-4444222022-2-2-2-2-2-2243−43000000-11-1100−2323−23230033−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-44-4-4444222022-2-2-2-2-2-22−4343000000-11-110023−2323−2300−3−3330000000000000000000000000000000000000000000000000000000000

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