Finite Group Databasebeta

← Group #13172273

Character table — Group #13172273

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666664444366666666666666644441212121212121212121212121212121244121212121212121212121212121212121212121244444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111-1-111-1-11111111-11-111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-11111111-1-1-1-1-1-1111111-1-1-1-1-1-111-111111-1-1-1-111111-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111-1-1-1-111111111-11-1-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-11-11-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-111-1-11111-1-11111-1-1111111-11-1-111-1-111-1-111-1-1-1-1-11111-1-1-1-1-111-1
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-11111-1-1-1-11111111111-1-1-1111-1-111-1-1-1-11111-1-1-1-1-111-1-11-1-11
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1111-1111111-1-1-11
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-11-11-1-1-1-111111-1
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11-11-11-1-1-1-11111-11
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111-1111-1111111-1-11-1
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1-111-1-11111-1-111-1-1-1-1-111-1-11-11-1
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-1-1-111-1-1-1-1111111111-111-1-111-1-111-1-111-1-1-11111-1-1-1-1-11-11
χ17222222-1222-122-1-1222-1-1222-1-122-1-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-12022000022-1-1222200-1-10000000-1-120000-1-1-1-1-1-1-1-10200200-1-1000-100
χ18222222-1222-122-1-1222-1-1222-1-122-1-1-1-10022-12-122-1-1-1-1-1-1-1-1-1-1-120-2-2000022-1-122-2-2001100000001-1-20000-1-1-1-111110-200-20011000100
χ19222222-1222-122-1-1222-1-1222-1-122-1-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20220000-2-211-2-22200-1-10000000-11200001111-1-1-1-10-200-20011000100
χ20222222-1222-122-1-1222-1-1222-1-122-1-1-1-100-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-20-2-20000-2-211-2-2-2-20011000000011-20000111111110200200-1-1000-100
χ21222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-10022-1-21-2-21111-1-1-11111-202-2000022-1-1-2-22200110000000-11-20000-1-111-1-1110-20020011000-100
χ22222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-10022-1-21-2-21111-1-1-11111-20-22000022-1-1-2-2-2-200-1-100000001120000-1-11111-1-10200-200-1-1000100
χ23222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-100-2-2-1-21-2-21111-1-1-11111202-20000-2-211222200110000000-1-1-2000011-1-1-1-1110200-200-1-1000100
χ24222222-1222-122-1-12-22-1-1-2-22-1-122-1-1-1-100-2-2-1-21-2-21111-1-1-1111120-220000-2-21122-2-200-1-100000001-12000011-1-111-1-10-20020011000-100
χ2522222-1222-12-1-12222-12-122-12-1-1-122-1-12200-1-12-1-122-1-1-1-1-1-1-1-1-102222222000000-1-1-1-122000000-120-1-1-1-1-10000-1-1-1-120020-1-10000-1000
χ2622222-1222-12-1-12222-12-122-12-1-1-122-1-12200-1-12-1-122-1-1-1-1-1-1-1-1-102-2-2222200000011-1-1-2-2000000-1-201-1-1-1-100001111-200-201100001000
χ2722222-1222-12-1-12222-12-122-12-1-1-122-1-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-10-222-2-2-2-2000000-1-11122000000120-111110000-1-1-1-1-200-201100001000
χ2822222-1222-12-1-12222-12-122-12-1-1-122-1-1-2-200-1-12-1-122-1-1-1-1-1-1-1-1-10-2-2-2-2-2-2-20000001111-2-20000001-20111110000111120020-1-10000-1000
χ2922222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-12200-11-211-2-211-1-1-111110-22-222-2-2000000-1-1-1-1-2-20000001201-1-1110000-1-111-20020-1-100001000
χ3022222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-12200-11-211-2-211-1-1-111110-2-2222-2-200000011-1-1220000001-20-1-1-111000011-1-1200-20110000-1000
χ3122222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-200-11-211-2-211-1-1-11111022-2-2-222000000-1-111-2-2000000-120111-1-10000-1-111200-20110000-1000
χ3222222-1222-12-1-1222-2-12-1-2-2-12-1-1-122-1-1-2-200-11-211-2-211-1-1-1111102-22-2-222000000111122000000-1-20-111-1-1000011-1-1-20020-1-100001000
χ332222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-1222222-122-1-1-1-122-1-1-1-1-1-1-12200-1-1-1-1-1-122-1-100220022-1-1-1-12020-1-1-1-1-1-1-1-10000002000000-1-10000
χ342222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-12222-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2200-1-1-1-111-2-211002200-2-2111120-20-1-1-1-11111000000-2000000110000
χ352222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-2-222-122-1-1-1-122-1-1-1-1-1-1-12-2001111-1-122-1-100-2-200-2-21111-20201111-1-1-1-1000000-2000000110000
χ362222-122-1-1222222-12-1-12-1-1-1-12-1-1-1-122-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2-200111111-2-21100-2-20022-1-1-1-1-20-20111111110000002000000-1-10000
χ372222-122-1-1222222-1-2-1-1211-1-12-1-1-1-1222222-1-2-21111-2-2-1-1-11111-2-200-1-111-1-1221100220022-1-1-1-1-20-20-1-111-1-111000000-2000000110000
χ382222-122-1-1222222-1-2-1-1211-1-12-1-1-1-12222-2-2-1-2-21111-2-2-1-1-111112-200-1-11111-2-2-1-1002200-2-21111-2020-1-11111-1-10000002000000-1-10000
χ392222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-2-222-1-2-21111-2-2-1-1-11111-220011-1-1-1-1221100-2-200-2-2111120-2011-1-1-1-1110000002000000-1-10000
χ402222-122-1-1222222-1-2-1-1211-1-12-1-1-1-122-2-2-2-2-1-2-21111-2-2-1-1-11111220011-1-111-2-2-1-100-2-20022-1-1-1-1202011-1-111-1-1000000-2000000110000
χ412-2-22222-2-2-2-22-22-2202220022-2-2-2-2-22-22i−2i2i−2i2000000002-2-2000000002i−2i002i−2i2i−2i00002i−2i002-222-2-200002i−2i002i−2i000000000000000000000
χ422-2-22222-2-2-2-22-22-2202220022-2-2-2-2-22-22i−2i−2i2i2000000002-2-2000000002i−2i00−2i2i−2i2i00002i−2i00-22-2-22200002i−2i00−2i2i000000000000000000000
χ432-2-22222-2-2-2-22-22-2202220022-2-2-2-2-22-2−2i2i2i−2i2000000002-2-200000000−2i2i002i−2i2i−2i0000−2i2i00-22-2-2220000−2i2i002i−2i000000000000000000000
χ442-2-22222-2-2-2-22-22-2202220022-2-2-2-2-22-2−2i2i−2i2i2000000002-2-200000000−2i2i00−2i2i−2i2i0000−2i2i002-222-2-20000−2i2i00−2i2i000000000000000000000
χ452-2-22-12211-2-22-22-2-10-1-12−i3i3-1-1-211112-22i−2i2i−2i-100−i3i3−i3i300-111−i3−i3i3i30000−ii3−3−ii2i−2i3−3002i−2i002-2-1-1110000−ii3−3−ii3−30000000000000−i3i30000
χ462-2-22-12211-2-22-22-2-10-1-12−i3i3-1-1-211112-22i−2i−2i2i-100−i3i3−i3i300-111−i3−i3i3i30000−ii3−3i−i−2i2i−33002i−2i00-2211-1-10000−ii3−3i−i−330000000000000i3−i30000
χ472-2-22-12211-2-22-22-2-10-1-12−i3i3-1-1-211112-2−2i2i2i−2i-100−i3i3−i3i300-111−i3−i3i3i30000i−i−33−ii2i−2i3−300−2i2i00-2211-1-10000i−i−33−ii3−30000000000000i3−i30000
χ482-2-22-12211-2-22-22-2-10-1-12−i3i3-1-1-211112-2−2i2i−2i2i-100−i3i3−i3i300-111−i3−i3i3i30000i−i−33i−i−2i2i−3300−2i2i002-2-1-1110000i−i−33i−i−330000000000000−i3i30000
χ492-2-22-12211-2-22-22-2-10-1-12i3−i3-1-1-211112-22i−2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i30000−ii−33−ii2i−2i−33002i−2i002-2-1-1110000−ii−33−ii−330000000000000i3−i30000
χ502-2-22-12211-2-22-22-2-10-1-12i3−i3-1-1-211112-22i−2i−2i2i-100i3−i3i3−i300-111i3i3−i3−i30000−ii−33i−i−2i2i3−3002i−2i00-2211-1-10000−ii−33i−i3−30000000000000−i3i30000
χ512-2-22-12211-2-22-22-2-10-1-12i3−i3-1-1-211112-2−2i2i2i−2i-100i3−i3i3−i300-111i3i3−i3−i30000i−i3−3−ii2i−2i−3300−2i2i00-2211-1-10000i−i3−3−ii−330000000000000−i3i30000
χ522-2-22-12211-2-22-22-2-10-1-12i3−i3-1-1-211112-2−2i2i−2i2i-100i3−i3i3−i300-111i3i3−i3−i30000i−i3−3i−i−2i2i3−300−2i2i002-2-1-1110000i−i3−3i−i3−30000000000000i3−i30000
χ5344444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-21100001-2-2-2-2-2-211111111100440000000000-2-200-2-20000000-20-2000000001111000000000000000
χ5444444-2-244-2-2-2-2-2-244-2-2144-2-21-2-2-2-21100001-2-2-2-2-2-211111111100-4-40000000000220022000000020200000000-1-1-1-1000000000000000
χ5544444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-21100001222222-1-1111-1-1-1-1004-40000000000-2-200220000000-2020000000011-1-1000000000000000
χ5644444-2-244-2-2-2-2-2-24-4-2-21-4-4-2-21-2-2-2-21100001222222-1-1111-1-1-1-100-4400000000002200-2-2000000020-200000000-1-111000000000000000
χ574444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-2004414-2-2-211-2-2111111140000000-2-2-2-2-2-200000000000000-20000011110000000000000000000
χ584444-24-2-2-24-244-2-2-24-21-2-2-2-21-2-2-211-2-200-4-414-2-2-211-2-21111111-4000000022222200000000000000200000-1-1-1-10000000000000000000
χ594444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-200441-4222-1-122111-1-1-1-1-40000000-2-2-2-2220000000000000020000011-1-10000000000000000000
χ604444-24-2-2-24-244-2-2-2-4-21-222-21-2-2-211-2-200-4-41-4222-1-122111-1-1-1-1400000002222-2-200000000000000-200000-1-1110000000000000000000
χ614444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-244001-2411-2-2-2-211111110400-2-2-2-200000000-2-200000000-2000111100000000000000000000000
χ624444-2-24-2-2-24-2-244-241-2-2-2-21-2-211-2-2-2-2-4-4001-2411-2-2-2-211111110-40022220000000022000000002000-1-1-1-100000000000000000000000
χ634444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-2440012-4-1-12222111-1-1-1-10-400-2-22200000000-2-200000000200011-1-100000000000000000000000
χ644444-2-24-2-2-24-2-244-2-41-2-2221-2-211-2-2-2-2-4-40012-4-1-12222111-1-1-1-1040022-2-2000000002200000000-2000-1-11100000000000000000000000
χ6544-4-44444-4-4-4-44-44-4044400-4-444-44-4-4-40000400000000-44-40000000000000000000000000000000000000000000000000000000000000
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χ814-44-4-2442-244-4-4-4-420-2-240022-42-22-2-440000-20000000022-20000000000000000000000000023−23−23230000000000000000000000000000000
χ824-44-4-2442-244-4-4-4-420-2-240022-42-22-2-440000-20000000022-200000000000000000000000000−232323−230000000000000000000000000000000
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χ844-4-4444-2-4-4-424-4-22404-2-2004-22-4-422-2200−4i4i-200000000-222000000000000−4i4i2i−2i00000000000000000000002i−2i000000000000000000000
χ854-4-444-24-4-42-4-224-440-24-200-24222-4-4-224i−4i00-200000000-222000000004i−4i0000000000−2i2i000000000000−2i2i0000000000000000000000000
χ864-4-444-24-4-42-4-224-440-24-200-24222-4-4-22−4i4i00-200000000-22200000000−4i4i00000000002i−2i0000000000002i−2i0000000000000000000000000
χ874-4-44-24-222-424-4-22-20-21-2−2i32i3-21222-1-1-22004i−4i100−2i32i3i3−i3001-1-1i3i3−i3−i300000000−2i2i−2i2i23−2300000000000000000000i−i−330000000000000000000
χ884-4-44-24-222-424-4-22-20-21-2−2i32i3-21222-1-1-2200−4i4i100−2i32i3i3−i3001-1-1i3i3−i3−i3000000002i−2i2i−2i−232300000000000000000000−ii3−30000000000000000000
χ894-4-44-24-222-424-4-22-20-21-22i3−2i3-21222-1-1-22004i−4i1002i3−2i3−i3i3001-1-1−i3−i3i3i300000000−2i2i−2i2i−232300000000000000000000i−i3−30000000000000000000
χ904-4-44-24-222-424-4-22-20-21-22i3−2i3-21222-1-1-2200−4i4i1002i3−2i3−i3i3001-1-1−i3−i3i3i3000000002i−2i2i−2i23−2300000000000000000000−ii−330000000000000000000
χ914-4-44-2-24222-4-224-4-201-2-2−2i32i31-22-1-122-224i−4i00100i3−i3−2i32i3001-1-1i3i3−i3−i30000−2i2i23−2300000000−2i2i000000000000i−i−3300000000000000000000000
χ924-4-44-2-24222-4-224-4-201-2-2−2i32i31-22-1-122-22−4i4i00100i3−i3−2i32i3001-1-1i3i3−i3−i300002i−2i−2323000000002i−2i000000000000−ii3−300000000000000000000000
χ934-4-44-2-24222-4-224-4-201-2-22i3−2i31-22-1-122-224i−4i00100−i3i32i3−2i3001-1-1−i3−i3i3i30000−2i2i−232300000000−2i2i000000000000i−i3−300000000000000000000000
χ944-4-44-2-24222-4-224-4-201-2-22i3−2i31-22-1-122-22−4i4i00100−i3i32i3−2i3001-1-1−i3−i3i3i300002i−2i23−23000000002i−2i000000000000−ii−3300000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-8-48-4-44-84-884-440-42-4004-2-4-442-2440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-48-444-84-4-88402-4-400-24-42-2-44440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-44444-44-44022200-2-222-22-2-2-20000-10000006-61-11-33-33000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-44444-44-44022200-2-222-22-2-2-20000-1000000-661-113-33-3000000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-4-88-4-44444-80-4-420044-24-44-4-220000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-44-48-4-8-84440-42-4004-244-4-224-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-484-4-4844-8-8402-4-400-244-224-44-40000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-44-4-4-444444022200-2-2-2-22-22-220000-10000000011-1−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-4-4-444444022200-2-2-2-22-22-220000-10000000011-13i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1068-8-888-4-4-8-844-44-4480-4-4200-4-4-244442-200002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44444-44-44-40222−4i34i322-2-2-2-2-22-20000-1002i3−2i32i3−2i300-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44444-44-44-402224i3−4i322-2-2-2-2-22-20000-100−2i32i3−2i32i300-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000

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