Finite Group Databasebeta

← Group #13169297

Character table — Group #13169297

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212224444441212121212121212121212121212121212121212446612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-11111111111-1-1111111-1-1-1-111111-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-111111111-1-1-1-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-11111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-11-1-111-1-111-1-111-1-11-111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11-1-1-11111-1-111-1-1-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1111-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111-11-1-1-111-1-11111-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1111-1-1-1-111-1-111-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-11-111-1-111-1-111-1-1111-111-1-1111-11-1
χ17222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1200200-1-1-1-1-1-1-1-122002222220000-1-1-1-120020000-1-1-1-1-1-1-1-100-1-100000000
χ18222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1200-200-1-1-1-111112200-2-2-2-2-2-200001111200-20000-1-1-1-11111001100000000
χ19222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-2002001111-1-1-1-1-2-20022-2-2-2-200001111-200200001111-1-1-1-1001100000000
χ20222222-12-1-122-12222-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-200-20011111111-2-200-2-222220000-1-1-1-1-200-200001111111100-1-100000000
χ21222222-12-1-122-12222-1-1-22-1-1-1-122-1-1112222-1-1-1-1-2-21111-2-21111-200-200-1-111-1-11122002222-2-200001111-200-20000-1-111-1-11100-1-100000000
χ22222222-12-1-122-12222-1-1-22-1-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-21111-200200-1-11111-1-12200-2-2-2-2220000-1-1-1-1-20020000-1-11111-1-1001100000000
χ23222222-12-1-122-12222-1-1-22-1-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-21111200-20011-1-1-1-111-2-20022-2-2220000-1-1-1-1200-2000011-1-1-1-111001100000000
χ24222222-12-1-122-12222-1-1-22-1-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-2111120020011-1-111-1-1-2-200-2-222-2-2000011112002000011-1-111-1-100-1-100000000
χ2522222-12222-1-122-12-12-12-12-12-1-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-122202222220000-1-1-1-100000000220000-1-120-1-1-1-1-1-1-1-100002000-1-100-1000
χ2622222-12222-1-122-12-12-12-12-12-1-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12-2-20-2-222220000-1-11100000000-2-20000-11-201111-1-1-1-10000-200011001000
χ2722222-12222-1-122-12-12-12-12-12-1-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-222022-2-2-2-2000011-1-100000000-2-200001-120-1-1-1-111110000-200011001000
χ2822222-12222-1-122-12-12-12-12-12-1-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-20-2-2-2-2-2-2000011110000000022000011-201111111100002000-1-100-1000
χ2922222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-22200-1-1-1-1-21-2-211111111-22-202222-2-20000-1-11100000000-2-200001-1-20-1-111-1-111000020001100-1000
χ3022222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-22200-1-1-1-1-21-2-211111111-2-220-2-222-2-20000-1-1-1-100000000220000112011-1-1-1-1110000-2000-1-1001000
χ3122222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-2-2-200-1-1-1-1-21-2-21111111122-2022-2-2220000111100000000220000-1-1-20-1-11111-1-10000-2000-1-1001000
χ3222222-12222-1-122-12-12-1-2-12-12-1-1-12-1-2-2-2-200-1-1-1-1-21-2-2111111112-220-2-2-2-222000011-1-100000000-2-20000-112011-1-111-1-1000020001100-1000
χ332222-122-122222-12-1-1-122-1-12-12-1-1-12220022-1-1-1-1-12-1-122-1-1-1-1-1-10222-1-1000022220022-1-100002200000002-1-1-1-1-1-10000-1-1-1-1020000-1-10-100
χ342222-122-122222-12-1-1-122-1-12-12-1-1-12220022-1-1-1-1-12-1-122-1-1-1-1-1-10-2-22110000222200-2-2-1-10000-2-20000000-21-111110000-1-1-1-10-20000110100
χ352222-122-122222-12-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1022-2-1-10000-2-2-2-20022110000-2-200000002-11-1-1-1-1000011110-20000110100
χ362222-122-122222-12-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-1-12-1-122-1-1-1-1-1-10-2-2-2110000-2-2-2-200-2-2110000220000000-211111100001111020000-1-10-100
χ372222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-11-211-2-211111102-2-2-1-1000022-2-200-2-2-1-10000220000000211-1-1110000-1-1110-20000-1-10100
χ382222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-11-211-2-21111110-22-211000022-2-20022-1-10000-2-20000000-2-1111-1-10000-1-111020000110-100
χ392222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-11-211-2-211111102-22-1-10000-2-22200-2-2110000-2-2000000021-1-1-111000011-1-1020000110-100
χ402222-122-122222-12-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-11-211-2-21111110-222110000-2-2220022110000220000000-2-1-111-1-1000011-1-10-20000-1-10100
χ412-22-2222-2-2-2-2-2222-22220-2-2-222-22-2-2002i−2i2i−2i2-2-220000000000000000002i−2i002i−2i002i−2i002i−2i2-20000000000000000002i−2i002i−2i00002-200000000
χ422-22-2222-2-2-2-2-2222-22220-2-2-222-22-2-2002i−2i−2i2i2-2-220000000000000000002i−2i00−2i2i002i−2i00−2i2i-220000000000000000002i−2i00−2i2i0000-2200000000
χ432-22-2222-2-2-2-2-2222-22220-2-2-222-22-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i002i−2i00−2i2i002i−2i-22000000000000000000−2i2i002i−2i0000-2200000000
χ442-22-2222-2-2-2-2-2222-22220-2-2-222-22-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i00−2i2i00−2i2i00−2i2i2-2000000000000000000−2i2i00−2i2i00002-200000000
χ452-22-222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−3−ii3−32i−2i002i−2i2-2000000−i3−i3i3i300000000−ii3−3−ii3−300-1100000000
χ462-22-222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000−ii3−3i−i−332i−2i00−2i2i-22000000i3i3−i3−i300000000−ii3−3i−i−33001-100000000
χ472-22-222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−33−ii3−3−2i2i002i−2i-22000000i3i3−i3−i300000000i−i−33−ii3−3001-100000000
χ482-22-222-1-211-2-2-122-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000i−i−33i−i−33−2i2i00−2i2i2-2000000−i3−i3i3i300000000i−i−33i−i−3300-1100000000
χ492-22-222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−33−ii−332i−2i002i−2i2-2000000i3i3−i3−i300000000−ii−33−ii−3300-1100000000
χ502-22-222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000−ii−33i−i3−32i−2i00−2i2i-22000000−i3−i3i3i300000000−ii−33i−i3−3001-100000000
χ512-22-222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−3−ii−33−2i2i002i−2i-22000000−i3−i3i3i300000000i−i3−3−ii−33001-100000000
χ522-22-222-1-211-2-2-122-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000i−i3−3i−i3−3−2i2i00−2i2i2-2000000i3i3−i3−i300000000i−i3−3i−i3−300-1100000000
χ532-2-22222-22-22-2-2-2-2222202-22-2-2-2-22-200000022-2-200000000000000000000000000000000002i−2i2i−2i2-22i−2i2i−2i000000000000000000002-22i−2i0000
χ542-2-22222-22-22-2-2-2-2222202-22-2-2-2-22-200000022-2-200000000000000000000000000000000002i−2i−2i2i-222i−2i2i−2i00000000000000000000-22−2i2i0000
χ552-2-22222-22-22-2-2-2-2222202-22-2-2-2-22-200000022-2-20000000000000000000000000000000000−2i2i2i−2i-22−2i2i−2i2i00000000000000000000-222i−2i0000
χ562-2-22222-22-22-2-2-2-2222202-22-2-2-2-22-200000022-2-20000000000000000000000000000000000−2i2i−2i2i2-2−2i2i−2i2i000000000000000000002-2−2i2i0000
χ5744444-2-24-2-2-2-2-24-24-2-214-2-21-21-2-2-21-2-2440011114-2-2-211-2-21111400000-2-2-2-20000-2-20000000000000000-2000000011110000000000000000
χ5844444-2-24-2-2-2-2-24-24-2-214-2-21-21-2-2-21-2-2-4-40011114-2-2-211-2-21111-4000002222000022000000000000000020000000-1-1-1-10000000000000000
χ5944444-2-24-2-2-2-2-24-24-2-21-4-2-21-21-2-2-212244001111-4222-1-122-1-1-1-1-400000-2-2220000-2-200000000000000002000000011-1-10000000000000000
χ6044444-2-24-2-2-2-2-24-24-2-21-4-2-21-21-2-2-2122-4-4001111-4222-1-122-1-1-1-140000022-2-20000220000000000000000-20000000-1-1110000000000000000
χ614444-24-2-2-2-244-2-24-2-21-24-21-21-2-2-21-2-2-200441111-2411-2-2-2-211110004000000-2-2-2-20000-2-2000000000000000-2000000001111000000000000
χ624444-24-2-2-2-244-2-24-2-21-24-21-21-2-2-21-2-2-200-4-41111-2411-2-2-2-21111000-40000002222000022000000000000000200000000-1-1-1-1000000000000
χ634444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-2-21-222004411112-4-1-12222-1-1-1-1000-4000000-2-2220000-2-200000000000000020000000011-1-1000000000000
χ644444-24-2-2-2-244-2-24-2-21-2-4-21-21-2-2-21-22200-4-411112-4-1-12222-1-1-1-1000400000022-2-2000022000000000000000-200000000-1-111000000000000
χ654444-2-24-244-2-24-2-2-21-2-241-2-2-2-211-2-24400001111-2-2-2-2-2-21111110440-2-20000000000-2-2000000000000000-2-20111100000000000000000000
χ664444-2-24-244-2-24-2-2-21-2-241-2-2-2-211-2-24400001111-2-2-2-2-2-21111110-4-4022000000000022000000000000000220-1-1-1-100000000000000000000
χ674444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-211-2-2-4-400001111222222-1-1-1-1-1-104-40-2-2000000000022000000000000000-22011-1-100000000000000000000
χ684444-2-24-244-2-24-2-2-21-2-2-41-2-2-2-211-2-2-4-400001111222222-1-1-1-1-1-10-440220000000000-2-20000000000000002-20-1-11100000000000000000000
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χ7844-4-4-2-24-2-442-2-42221-2-20-1-22221-12-20000001-11-1000000−3i3i−3i3i−3i3i0000−2i32i30000000000−2323000000000000000000i3−i33−300000000000000000000
χ7944-4-4-2-24-2-442-2-42221-2-20-1-22221-12-20000001-11-1000000−3i3i−3i3i−3i3i00002i3−2i3000000000023−23000000000000000000−i3i3−3300000000000000000000
χ804-44-44-24-4-4-42244-2-4-24-202-424-22-2-42004i−4i00-222-20000000000000000004i−4i000000−2i2i000000000000000000000000−2i2i000000000000000000
χ814-44-44-24-4-4-42244-2-4-24-202-424-22-2-4200−4i4i00-222-2000000000000000000−4i4i0000002i−2i0000000000000000000000002i−2i000000000000000000
χ824-44-44-2-2-42222-24-2-4-2-21022-1-212-22-1−2i32i34i−4i001-1-1100−2i32i3i3−i300i3i3−i3−i3000000−2i2i23−230000−2i2i000000000000000000000000i−i−330000000000000000
χ834-44-44-2-2-42222-24-2-4-2-21022-1-212-22-1−2i32i3−4i4i001-1-1100−2i32i3i3−i300i3i3−i3−i30000002i−2i−232300002i−2i000000000000000000000000−ii3−30000000000000000
χ844-44-44-2-2-42222-24-2-4-2-21022-1-212-22-12i3−2i34i−4i001-1-11002i3−2i3−i3i300−i3−i3i3i3000000−2i2i−23230000−2i2i000000000000000000000000i−i3−30000000000000000
χ854-44-44-2-2-42222-24-2-4-2-21022-1-212-22-12i3−2i3−4i4i001-1-11002i3−2i3−i3i300−i3−i3i3i30000002i−2i23−2300002i−2i000000000000000000000000−ii−330000000000000000
χ864-44-4-2442-4-4-4-44-242-2-24022-4-242-22-400004i−4i-222-200000000000000000000004i−4i000000−2i2i000000000000000000000000−2i2i00000000000000
χ874-44-4-2442-4-4-4-44-242-2-24022-4-242-22-40000−4i4i-222-20000000000000000000000−4i4i0000002i−2i0000000000000000000000002i−2i00000000000000
χ884-44-4-24-2222-4-4-2-242-21-202-121-22-2-12−2i32i3004i−4i1-1-1100i3−i3−2i32i300i3i3−i3−i30000000000−2i2i23−230000−2i2i000000000000000000000000i−i−33000000000000
χ894-44-4-24-2222-4-4-2-242-21-202-121-22-2-12−2i32i300−4i4i1-1-1100i3−i3−2i32i300i3i3−i3−i300000000002i−2i−232300002i−2i000000000000000000000000−ii3−3000000000000
χ904-44-4-24-2222-4-4-2-242-21-202-121-22-2-122i3−2i3004i−4i1-1-1100−i3i32i3−2i300−i3−i3i3i30000000000−2i2i−23230000−2i2i000000000000000000000000i−i3−3000000000000
χ914-44-4-24-2222-4-4-2-242-21-202-121-22-2-122i3−2i300−4i4i1-1-1100−i3i32i3−2i300−i3−i3i3i300000000002i−2i23−2300002i−2i000000000000000000000000−ii−33000000000000
χ924-4-4444-2-4-224-42-4-444-2-2042-222-4-4-22000000-2-22200000000000000000000000000000000004i−4i0000−2i2i−2i2i0000000000000000000000000000
χ934-4-4444-2-4-224-42-4-444-2-2042-222-4-4-22000000-2-2220000000000000000000000000000000000−4i4i00002i−2i2i−2i0000000000000000000000000000
χ944-4-444-24-44-4-22-4-424-24-20-2-4-2-422242000000-2-222000000000000000000000000000000000000004-4000000000000000000000000-22000000
χ954-4-444-24-44-4-22-4-424-24-20-2-4-2-422242000000-2-22200000000000000000000000000000000000000-440000000000000000000000002-2000000
χ964-4-44-24424-44-4-42-4-2-2-240-2242-422-2-4000000-2-2220000000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i0000
χ974-4-44-24424-44-4-42-4-2-2-240-2242-422-2-4000000-2-222000000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i0000
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
χ10088-8-88-4-484-44-44-84-8-4-4204-4-24-2-44420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-44-4-8844-84-42-40424-24-44-2-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-44-44-444442220-22-2-2-22-2-22000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-44-44-444442220-22-2-2-22-2-22000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-484-8-8448-4-442-4-40-244-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444444-4-4-442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444444-4-4-442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-8-44-444-848-4-420-4424-244-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-44-448-844-8-4-42-40-4-2-4-24442400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4848-8-44-844-42-4-4024-444-2-2-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-44-44444-422202-22-2-2-2-22-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-44-44444-422202-22-2-2-2-22-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000

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