Finite Group Databasebeta

← Group #13169453

Character table — Group #13169453

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212441212121212121212121212121212121212121212244446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1111111111-1-11-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111111111111-1-1-1-1-11-11-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11-11-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-11111-1-1-1-11111-1-11-11-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-111-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-111-1-111-1-111111111-11-1-111-1-111-1-111-1-1-1-1-111-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1111111111111-1-11-1-1-11111-1-111-1-1-111-1-1-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111-111-1111111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1111-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-111-1-1111-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-111-1111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-1-111-111-1-1-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-111-1-111-1-11111111-111-1-111-1-111-1-111-1-1-111-1-1-1-1111-1-11
χ17222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-122002222-1-1-1-120020000-1-1-1-1-1-1-1-120000-1-100000000
χ18222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-12-20000-1-1-1-11111-2-20022-2-21111-20020000-1-1-1-11111-200001100000000
χ19222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-2200001111-1-1-1-12200-2-2-2-21111200-200001111-1-1-1-1-200001100000000
χ20222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-2-2000011111111-2-200-2-222-1-1-1-1-200-200001111111120000-1-100000000
χ21222222-12-1-122-12222-1-1-22-1-1-1-122-1-1112222-1-1-1-1-2-21111-2-21111-2-20000-1-111-1-11122002222-1-1-1-1-200-20000-1-111-1-111-200001100000000
χ22222222-12-1-122-12222-1-1-22-1-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-21111-220000-1-11111-1-1-2-20022-2-21111200-20000-1-11111-1-120000-1-100000000
χ23222222-12-1-122-12222-1-1-22-1-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-211112-2000011-1-1-1-1112200-2-2-2-21111-2002000011-1-1-1-11120000-1-100000000
χ24222222-12-1-122-12222-1-1-22-1-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-2111122000011-1-111-1-1-2-200-2-222-1-1-1-12002000011-1-111-1-1-200001100000000
χ2522222-12222-1-122-12-12-12-12-12-1-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-102222200002222-1-1-1-100000000-1-120-1-1-1-10000-1-1-1-10020200-1-100-1000
χ2622222-12222-1-122-12-12-12-12-12-1-1-12-1220022-1-1-1-12-122-1-1-1-1-1-1-1-102-2-2-2-200002222-1-11100000000-11-2011110000-1-1-1-100-20-20011001000
χ2722222-12222-1-122-12-12-12-12-12-1-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-222220000-2-2-2-211-1-1000000001-120-1-1-1-10000111100-20-20011001000
χ2822222-12222-1-122-12-12-12-12-12-1-1-12-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-2-2-20000-2-2-2-211110000000011-201111000011110020200-1-100-1000
χ2922222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-1-21-2-2111111110-22-222000022-2-2-1-111000000001-1-20-1-1110000-1-11100-202001100-1000
χ3022222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-1-21-2-2111111110-2-22-2-2000022-2-2-1-1-1-100000000112011-1-10000-1-1110020-200-1-1001000
χ3122222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-1-21-2-211111111022-2220000-2-222111100000000-1-1-20-1-111000011-1-10020-200-1-1001000
χ3222222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-1-21-2-21111111102-22-2-20000-2-22211-1-100000000-112011-1-1000011-1-100-202001100-1000
χ332222-122-122222-12-1-1-122-1-12-12-1-1-12222200-1-1-1-1-12-1-122-1-1-1-1-1-12022-1-1222200000022-1-100000002-1-1-1-1-1-1-1-1-1-10000020200000-1-10-100
χ342222-122-122222-12-1-1-122-1-12-12-1-1-12222200-1-1-1-1-12-1-122-1-1-1-1-1-120-2-2112222000000-2-2-1-10000000-21-11111-1-1-1-100000-20-200000110100
χ352222-122-122222-12-1-1-122-1-12-12-1-1-1222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2022-1-1-2-2-2-2000000221100000002-11-1-1-1-1111100000-20-200000110100
χ362222-122-122222-12-1-1-122-1-12-12-1-1-1222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-211-2-2-2-2000000-2-2110000000-211111111110000020200000-1-10-100
χ372222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-11-211-2-2111111-202-2-1-122-2-2000000-2-2-1-10000000211-1-111-1-11100000-20200000-1-10100
χ382222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-11-211-2-2111111-20-221122-2-200000022-1-10000000-2-1111-1-1-1-1110000020-200000110-100
χ392222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-11-211-2-2111111202-2-1-1-2-222000000-2-211000000021-1-1-11111-1-10000020-200000110-100
χ402222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-11-211-2-211111120-2211-2-22200000022110000000-2-1-111-1-111-1-100000-20200000-1-10100
χ412-2-22222-2-2-2-2-2222-22220-2-2-222-22-2-2002i−2i2i−2i2-2-220000000000000000002i−2i002i−2i002i−2i002i−2i2-222-2-2000000002i−2i002i−2i00000000000000000
χ422-2-22222-2-2-2-2-2222-22220-2-2-222-22-2-2002i−2i−2i2i2-2-220000000000000000002i−2i00−2i2i00−2i2i002i−2i-22-2-222000000002i−2i00−2i2i00000000000000000
χ432-2-22222-2-2-2-2-2222-22220-2-2-222-22-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i002i−2i002i−2i00−2i2i-22-2-22200000000−2i2i002i−2i00000000000000000
χ442-2-22222-2-2-2-2-2222-22220-2-2-222-22-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i00−2i2i00−2i2i00−2i2i2-222-2-200000000−2i2i00−2i2i00000000000000000
χ452-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−3−ii3−32i−2i002i−2i2-2-1-11100000000−ii3−3−ii3−300000−i3i300000000
χ462-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−3i−i−33−2i2i002i−2i-2211-1-100000000−ii3−3i−i−3300000i3−i300000000
χ472-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−33−ii3−32i−2i00−2i2i-2211-1-100000000i−i−33−ii3−300000i3−i300000000
χ482-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−33i−i−33−2i2i00−2i2i2-2-1-11100000000i−i−33i−i−3300000−i3i300000000
χ492-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−33−ii−332i−2i002i−2i2-2-1-11100000000−ii−33−ii−3300000i3−i300000000
χ502-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−33i−i3−3−2i2i002i−2i-2211-1-100000000−ii−33i−i3−300000−i3i300000000
χ512-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−3−ii−332i−2i00−2i2i-2211-1-100000000i−i3−3−ii−3300000−i3i300000000
χ522-2-2222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−3i−i3−3−2i2i00−2i2i2-2-1-11100000000i−i3−3i−i3−300000i3−i300000000
χ5344444-2-24-2-2-2-2-24-24-2-214-2-21-21-2-2-21-2-2004411114-2-2-211-2-211110400000000-2-2-2-2-2-20000000000-2000000000001111000000000000000
χ5444444-2-24-2-2-2-2-24-24-2-214-2-21-21-2-2-21-2-200-4-411114-2-2-211-2-211110-4000000002222220000000000200000000000-1-1-1-1000000000000000
χ5544444-2-24-2-2-2-2-24-24-2-21-4-2-21-21-2-2-212200441111-4222-1-122-1-1-1-10-400000000-2-222-2-2000000000020000000000011-1-1000000000000000
χ5644444-2-24-2-2-2-2-24-24-2-21-4-2-21-21-2-2-212200-4-41111-4222-1-122-1-1-1-1040000000022-2-2220000000000-200000000000-1-111000000000000000
χ574444-24-2-2-2-244-2-24-2-21-24-21-21-2-2-21-2-2-244001111-2411-2-2-2-21111400000-2-2-2-200000000-2-2000000000-2000011110000000000000000000
χ584444-24-2-2-2-244-2-24-2-21-24-21-21-2-2-21-2-2-2-4-4001111-2411-2-2-2-21111-4000002222000000002200000000020000-1-1-1-10000000000000000000
χ594444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-2-21-222440011112-4-1-12222-1-1-1-1-400000-2-22200000000-2-20000000002000011-1-10000000000000000000
χ604444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-2-21-222-4-40011112-4-1-12222-1-1-1-140000022-2-20000000022000000000-20000-1-1110000000000000000000
χ614444-2-24-244-2-24-2-2-21-2-241-2-2-2-211-2-24400001111-2-2-2-2-2-21111110044-2-20000000000-2-2000000000-2-20111100000000000000000000000
χ624444-2-24-244-2-24-2-2-21-2-241-2-2-2-211-2-24400001111-2-2-2-2-2-211111100-4-422000000000022000000000220-1-1-1-100000000000000000000000
χ634444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-211-2-2-4-400001111222222-1-1-1-1-1-1004-4-2-2000000000022000000000-22011-1-100000000000000000000000
χ644444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-211-2-2-4-400001111222222-1-1-1-1-1-100-44220000000000-2-20000000002-20-1-11100000000000000000000000
χ6544-4-4444-44-44-4-4-4-4444404-44-4-4-4-44-400000044-4-4000000000000000000000000000000000000000000000000000000000000000000000
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χ804-44-4-2-24-2-442-2-42221-2-20-1-22221-12-20000001-11-10000003i−3i3i−3i3i−3i00002i3−2i30000000000−2323000000000000−i3i33−300000000000000000000000
χ814-44-4-2-24-2-442-2-42221-2-20-1-22221-12-20000001-11-1000000−3i3i−3i3i−3i3i0000−2i32i30000000000−2323000000000000i3−i33−300000000000000000000000
χ824-44-4-2-24-2-442-2-42221-2-20-1-22221-12-20000001-11-1000000−3i3i−3i3i−3i3i00002i3−2i3000000000023−23000000000000−i3i3−3300000000000000000000000
χ834-4-444-24-4-4-42244-2-4-24-202-424-22-2-4200004i−4i-222-200000000000000000000004i−4i00−2i2i0000000000000000000000−2i2i00000000000000000
χ844-4-444-24-4-4-42244-2-4-24-202-424-22-2-420000−4i4i-222-20000000000000000000000−4i4i002i−2i00000000000000000000002i−2i00000000000000000
χ854-4-444-2-2-42222-24-2-4-2-21022-1-212-22-1−2i32i3004i−4i1-1-1100−2i32i3i3−i300i3i3−i3−i30000000000−2i2i23−23−2i2i0000000000000000000000i−i−33000000000000000
χ864-4-444-2-2-42222-24-2-4-2-21022-1-212-22-1−2i32i300−4i4i1-1-1100−2i32i3i3−i300i3i3−i3−i300000000002i−2i−23232i−2i0000000000000000000000−ii3−3000000000000000
χ874-4-444-2-2-42222-24-2-4-2-21022-1-212-22-12i3−2i3004i−4i1-1-11002i3−2i3−i3i300−i3−i3i3i30000000000−2i2i−2323−2i2i0000000000000000000000i−i3−3000000000000000
χ884-4-444-2-2-42222-24-2-4-2-21022-1-212-22-12i3−2i300−4i4i1-1-11002i3−2i3−i3i300−i3−i3i3i300000000002i−2i23−232i−2i0000000000000000000000−ii−33000000000000000
χ894-4-44-2442-4-4-4-44-242-2-24022-4-242-22-4004i−4i00-222-20000000000000000004i−4i0000000000−2i2i00000000000000−2i2i000000000000000000000
χ904-4-44-2442-4-4-4-44-242-2-24022-4-242-22-400−4i4i00-222-2000000000000000000−4i4i00000000002i−2i000000000000002i−2i000000000000000000000
χ914-4-44-24-2222-4-4-2-242-21-202-121-22-2-12−2i32i34i−4i001-1-1100i3−i3−2i32i300i3i3−i3−i3000000−2i2i23−2300000000−2i2i00000000000000i−i−330000000000000000000
χ924-4-44-24-2222-4-4-2-242-21-202-121-22-2-12−2i32i3−4i4i001-1-1100i3−i3−2i32i300i3i3−i3−i30000002i−2i−2323000000002i−2i00000000000000−ii3−30000000000000000000
χ934-4-44-24-2222-4-4-2-242-21-202-121-22-2-122i3−2i34i−4i001-1-1100−i3i32i3−2i300−i3−i3i3i3000000−2i2i−232300000000−2i2i00000000000000i−i3−30000000000000000000
χ944-4-44-24-2222-4-4-2-242-21-202-121-22-2-122i3−2i3−4i4i001-1-1100−i3i32i3−2i300−i3−i3i3i30000002i−2i23−23000000002i−2i00000000000000−ii−330000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-8-44-444-848-4-420-4424-244-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-44-448-844-8-4-42-40-4-2-4-24442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4848-8-44-844-42-4-4024-444-2-2-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-44-44444-422202-22-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-44-44444-422202-22-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-484-44-44-84-8-4-4204-4-24-2-44420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4-44-4-8844-84-42-40424-24-44-2-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-44-44-444442220-22-2-2-22-2-22000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4-44-44-444442220-22-2-2-22-2-22000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-8-8448-4-442-4-40-244-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-4-442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-4-442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000

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