Finite Group Databasebeta

← Group #13168626

Character table — Group #13168626

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212222466666612121212121212121212224444441212121266666666612121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-1-1-111111111111111-1-111-1-11111-11-111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-11-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-111-1-1-1-1-111-1-1-1-11-1-1-1-1-1111-111
χ51111111111111111111111111111111-1-1111111111111111111-11111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-11-1-111111-1-111111-1-1-1-1-1111-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-11-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11-1-111-1-1-111-1-111-1111-1-111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-111-1-1111-11111-1-11-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-11-1-111-1-111111-1-111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111111111111-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111111111-1111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1111111-111-1-111-1-1-1-1-11111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11-11111-1-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1111-1-111-1-1-1111-1-111-11-11
χ17222222-122-1-12222-1-1-122-1-122-12-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-120020000-1-1-1-1-1-12222-1-122002200-1-1-1-1020-1-100002-1-1-1-1-1-100-1-100000000
χ18222222-122-1-12222-1-1-122-1-122-12-1-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-1200-20000-1-1-1-11122-2-211-2-200-2-2001111020-1-10000-2-1-11111001100000000
χ19222222-122-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1-200200001111-1-1-2-222-1-1-2-200-2-20011110-20110000211-1-1-1-1001100000000
χ20222222-122-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-200-20000111111-2-2-2-21122002200-1-1-1-10-20110000-211111100-1-100000000
χ21222222-122-1-12222-1-1-12-2-1-122-12-1-1-1112222-1-1-1-1-2-2-2-211111111-200-2000011-1-1112222-1-12200-2-20011110-20110000-2-1-111-1-100-1-100000000
χ22222222-122-1-12222-1-1-12-2-1-122-12-1-1-11122-2-2-1-1-1-1-2-2-2-211111111-2002000011-1-1-1-122-2-211-2-2002200-1-1-1-10-201100002-1-1-1-111001100000000
χ23222222-122-1-12222-1-1-12-2-1-122-12-1-1-111-2-222-1-1-1-1-2-2-2-211111111200-20000-1-11111-2-222-1-1-2-2002200-1-1-1-1020-1-10000-21111-1-1001100000000
χ24222222-122-1-12222-1-1-12-2-1-122-12-1-1-111-2-2-2-2-1-1-1-1-2-2-2-21111111120020000-1-111-1-1-2-2-2-2112200-2-2001111020-1-10000211-1-11100-1-100000000
χ2522222-12-12222-1-1222-1-122-1-1-1-1-12-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1222022-1-1222200-1-100000022000000002-1-1-1-1-1-1-1-10-1-100000200-1-1000-100
χ2622222-12-12222-1-1222-1-122-1-1-1-1-12-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12-2-20-2-211222200-1-1000000-2-200000000-2-11-1-111110-1-100000-20011000100
χ2722222-12-12222-1-1222-1-122-1-1-1-1-12-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-222022-1-1-2-2-2-20011000000-2-20000000021-111-1-1-1-101100000-20011000100
χ2822222-12-12222-1-1222-1-122-1-1-1-1-12-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-20-2-211-2-2-2-200110000002200000000-21111111101100000200-1-1000-100
χ2922222-12-12222-1-1222-1-1-22-1-1-1-1-12-12-2-22200-1-1-1-11-21111-2-21111-22-202211-2-22200-1-1000000-2-200000000-21-111-1-1110-1-10000020011000-100
χ3022222-12-12222-1-1222-1-1-22-1-1-1-1-12-12-2-22200-1-1-1-11-21111-2-21111-2-220-2-2-1-1-2-22200-1-100000022000000002111111-1-10-1-100000-200-1-1000100
χ3122222-12-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-2-200-1-1-1-11-21111-2-2111122-20221122-2-200110000002200000000-2-1-1-1-1-1-11101100000-200-1-1000100
χ3222222-12-12222-1-1222-1-1-22-1-1-1-1-12-12-2-2-2-200-1-1-1-11-21111-2-211112-220-2-2-1-122-2-20011000000-2-2000000002-11-1-111-1-10110000020011000-100
χ332222-1222-122-122-12-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-10222-1-12200002200-1-122000000220000-10200-1-1-1-1-100-1-1-1-1200000-1-1-1000
χ342222-1222-122-122-12-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2211-2-200002200-1-122000000-2-2000010-2001111-100-1-1-1-1-200000111000
χ352222-1222-122-122-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1022-2-1-1220000-2-20011-2-2000000-2-20000-10200-1-1-1-11001111-200000111000
χ362222-1222-122-122-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-211-2-20000-2-20011-2-200000022000010-20011111001111200000-1-1-1000
χ372222-1222-122-122-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-211111102-2-2-1-1-2-20000-2-200-1-12200000022000010200-1-11110011-1-1-200000-1-11000
χ382222-1222-122-122-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-21111110-22-211220000-2-200-1-122000000-2-20000-10-20011-1-110011-1-120000011-1000
χ392222-1222-122-122-12-12-1-2-12-1-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-211111102-22-1-1-2-20000220011-2-2000000-2-2000010200-1-111-100-1-11120000011-1000
χ402222-1222-122-122-12-12-1-2-12-1-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-21111110-22211220000220011-2-2000000220000-10-20011-1-1-100-1-111-200000-1-11000
χ4122-2-2222-2-22-22-22-2-222202-22-2-2-2-22-200000022-2-200000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i000000000000000000002-22i−2i0000
χ4222-2-2222-2-22-22-22-2-222202-22-2-2-2-22-200000022-2-200000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i000000000000000000002-2−2i2i0000
χ4322-2-2222-2-22-22-22-2-222202-22-2-2-2-22-200000022-2-20000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i00000000000000000000-22−2i2i0000
χ4422-2-2222-2-22-22-22-2-222202-22-2-2-2-22-200000022-2-20000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i00000000000000000000-222i−2i0000
χ452-2-2222222-22-2-2-2-2-22220-22-22-2-22-2-2002i−2i2i−2i2-22-200000000000000000000002i−2i002i−2i2i−2i2i−2i2-2000000000000000000002i−2i002i−2i002-200000000
χ462-2-2222222-22-2-2-2-2-22220-22-22-2-22-2-2002i−2i−2i2i2-22-200000000000000000000002i−2i002i−2i−2i2i−2i2i-22000000000000000000002i−2i00−2i2i00-2200000000
χ472-2-2222222-22-2-2-2-2-22220-22-22-2-22-2-200−2i2i2i−2i2-22-20000000000000000000000−2i2i00−2i2i2i−2i2i−2i-2200000000000000000000−2i2i002i−2i00-2200000000
χ482-2-2222222-22-2-2-2-2-22220-22-22-2-22-2-200−2i2i−2i2i2-22-20000000000000000000000−2i2i00−2i2i−2i2i−2i2i2-200000000000000000000−2i2i00−2i2i002-200000000
χ492-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-1113−32i−2i2i−2i-11-1100003−33−333−3−300000000−i3i3−ii−i3i32i−2i2i−2i−ii2-20000003−33−3000−i3i300000−ii−i3i3−ii00-1100000000
χ502-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-1113−32i−2i−2i2i-11-1100003−33−333−3−300000000−i3i3−iii3−i32i−2i−2i2ii−i-22000000−33−33000−i3i300000−iii3−i3i−i001-100000000
χ512-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-1113−3−2i2i2i−2i-11-1100003−33−333−3−300000000i3−i3i−i−i3i3−2i2i2i−2i−ii-22000000−33−33000i3−i300000i−i−i3i3−ii001-100000000
χ522-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-1113−3−2i2i−2i2i-11-1100003−33−333−3−300000000i3−i3i−ii3−i3−2i2i−2i2ii−i2-20000003−33−3000i3−i300000i−ii3−i3i−i00-1100000000
χ532-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-111−332i−2i2i−2i-11-110000−33−33−3−33300000000i3−i3−iii3−i32i−2i2i−2i−ii2-2000000−33−33000i3−i300000−iii3−i3−ii00-1100000000
χ542-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-111−332i−2i−2i2i-11-110000−33−33−3−33300000000i3−i3−ii−i3i32i−2i−2i2ii−i-220000003−33−3000i3−i300000−ii−i3i3i−i001-100000000
χ552-2-2222-1221-1-2-2-2-21-1-1201-1-221-2-111−33−2i2i2i−2i-11-110000−33−33−3−33300000000−i3i3i−ii3−i3−2i2i2i−2i−ii-220000003−33−3000−i3i300000i−ii3−i3−ii001-100000000
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χ5744444-2-2-24-2-24-2-24-2-21-24-21-2-21-2-21-2-2-244001111-24-2-211-2-2111140000000-2-2-2-200-2-200000000000000000-201100000110000000000000000
χ5844444-2-2-24-2-24-2-24-2-21-24-21-2-21-2-21-2-2-2-4-4001111-24-2-211-2-21111-40000000222200220000000000000000020-1-100000-1-10000000000000000
χ5944444-2-2-24-2-24-2-24-2-21-2-4-21-2-21-2-21-222440011112-422-1-122-1-1-1-1-4000000022-2-200-2-20000000000000000020-1-100000110000000000000000
χ6044444-2-2-24-2-24-2-24-2-21-2-4-21-2-21-2-21-222-4-40011112-422-1-122-1-1-1-140000000-2-222002200000000000000000-201100000-1-10000000000000000
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χ624444-24-24-2-2-2-244-2-21-2-241-2-2-2-2-21-21-2-200-4-411114-2-2-2-2-2111111000-40000000022002222000000000000000000000200-1-1-1-1000000000000
χ634444-24-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-212200441111-422222-1-1-1-1-1-1000-4000000002200-2-2-2-2000000000000000000000200-1-111000000000000
χ644444-24-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-212200-4-41111-422222-1-1-1-1-1-1000400000000-2-2002222000000000000000000000-20011-1-1000000000000
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χ894-4-444-2-2-242-2-422-42-21-20212-2-12-2-1223−23−4i4i001-11-10000−3323−23−3−333000000002i3−2i32i−2i002i−2i0000000000000000000−i3i300000−ii0000000000000000
χ904-4-444-2-2-242-2-422-42-21-20212-2-12-2-12−23234i−4i001-11-100003−3−232333−3−3000000002i3−2i3−2i2i00−2i2i0000000000000000000−i3i300000i−i0000000000000000
χ914-4-444-2-2-242-2-422-42-21-20212-2-12-2-12−2323−4i4i001-11-100003−3−232333−3−300000000−2i32i32i−2i002i−2i0000000000000000000i3−i300000−ii0000000000000000
χ924-4-44-2444-2-442-4-42-4-24-20242-2-42-2-4200004i−4i-22-220000000000000000000000000000−2i2i4i−4i00000000000000000000000000−2i2i000000000000
χ934-4-44-2444-2-442-4-42-4-24-20242-2-42-2-420000−4i4i-22-2200000000000000000000000000002i−2i−4i4i000000000000000000000000002i−2i000000000000
χ944-4-44-24-24-22-22-4-4221-2-20-1-22-22212-123−23004i−4i1-11-1000023−23−33−3−333000000000000−2i32i300−2i2i−2i2i000000000000000000000000i3−i3i−i000000000000
χ954-4-44-24-24-22-22-4-4221-2-20-1-22-22212-123−2300−4i4i1-11-1000023−23−33−3−3330000000000002i3−2i3002i−2i2i−2i000000000000000000000000−i3i3−ii000000000000
χ964-4-44-24-24-22-22-4-4221-2-20-1-22-22212-1−2323004i−4i1-11-10000−23233−333−3−30000000000002i3−2i300−2i2i−2i2i000000000000000000000000−i3i3i−i000000000000
χ974-4-44-24-24-22-22-4-4221-2-20-1-22-22212-1−232300−4i4i1-11-10000−23233−333−3−3000000000000−2i32i3002i−2i2i−2i000000000000000000000000i3−i3−ii000000000000
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
χ10088-8-88-4-44-8-4484-4-84-42-40-4-2-44-2442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-84-44-4-88442-4-4024-4444-2-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48448-8-44-44-8-4-420-442-24-24-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-44-44-44422202-22-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-444-44-44-44422202-22-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-44-844-8-448-4-42-404-2442-44-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-844448-8-4-42-4-40-2444-4-4-2420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444444-44-4-42220-2-2-2-222-2-22000000-111-1006-60000-33-33000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-444444-44-4-42220-2-2-2-222-2-22000000-111-100-6600003-33-3000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-4-4-884444-8-4-4204-4-224-2-4440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4-44-4444442220-22-22-2-22-2-243−430000-11-110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4-44-4444442220-22-22-2-22-2-2−43430000-11-11000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000

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