Finite Group Databasebeta

← Group #13169279

Character table — Group #13169279

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212444412121212121212121212121212121212226666121212121212121212121212121212122444412121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111-1-11-1-1-1-111111111-1-11-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-111111111-1-1-1-111-1-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-111111111111111111111-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-111-1-111111111-11-1-111-1-111-1-111-1-11-1-11-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-111-1-111111111-1-11-1-1-11111-1-111-1-1-11-1-11-1-111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-1111-11-1111-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1111-1111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11-11-1-1-111-1-11111-1-11-11-1111-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111-1-111-1-111111111-1111-1-1-1-111-1-111-11-1-11-1-111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111-1-11111111-111-1-111-1-111-1-1111-1-11-1-1-1-1-1111-11-1
χ17222222-122-1-122-1222-1-122-1-12-1-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-1222022-1-1-1-12222000000000000-1-120-1-1-1-1-1-1-1-100002200000-1-100-1000
χ18222222-122-1-122-1222-1-122-1-12-1-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-220-2-211-1-12222000000000000-11-201111-1-1-1-10000-2-20000011001000
χ19222222-122-1-122-1222-1-122-1-12-1-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-122-2022-1-111-2-2-2-20000000000001-120-1-1-1-111110000-2-20000011001000
χ20222222-122-1-122-1222-1-122-1-12-1-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-20-2-21111-2-2-2-200000000000011-201111111100002200000-1-100-1000
χ21222222-122-1-122-1222-1-1-22-1-12-1-1-12-1-2-22200-1-1-1-11-2-2-2111111112-2-202211-1-122-2-20000000000001-1-20-1-111-1-11100002-2000001100-1000
χ22222222-122-1-122-1222-1-1-22-1-12-1-1-12-1-2-22200-1-1-1-11-2-2-211111111-22-20-2-2-1-1-1-122-2-2000000000000112011-1-1-1-1110000-2200000-1-1001000
χ23222222-122-1-122-1222-1-1-22-1-12-1-1-12-1-2-2-2-200-1-1-1-11-2-2-2111111112-220221111-2-222000000000000-1-1-20-1-11111-1-10000-2200000-1-1001000
χ24222222-122-1-122-1222-1-1-22-1-12-1-1-12-1-2-2-2-200-1-1-1-11-2-2-211111111-2220-2-2-1-111-2-222000000000000-112011-1-111-1-100002-2000001100-1000
χ2522222-12-1222-1-1222-12-12-12-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-10022000022-1-1-1-1-1-1-1-12222-1-1-1-120020000-1-1-1-1-1-1-1-100200-1-100000000
χ2622222-12-1222-1-1222-12-12-12-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1002-2000022-1-1-1-11111-2-2-2-21111200-20000-1-1-1-1111100-2001100000000
χ2722222-12-1222-1-1222-12-12-12-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-100-220000-2-21111-1-1-1-122-2-21111-200200001111-1-1-1-100-2001100000000
χ2822222-12-1222-1-1222-12-12-12-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-100-2-20000-2-211111111-2-222-1-1-1-1-200-200001111111100200-1-100000000
χ2922222-12-1222-1-1222-12-1-2-12-1-1-122-1-1112222-1-1-1-1-2-21111-2-2111100-2-2000022-1-111-1-1112222-1-1-1-1-200-20000-1-111-1-11100-2001100000000
χ3022222-12-1222-1-1222-12-1-2-12-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-2111100-22000022-1-11111-1-1-2-2-2-21111-20020000-1-11111-1-100200-1-100000000
χ3122222-12-1222-1-1222-12-1-2-12-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-21111002-20000-2-211-1-1-1-11122-2-21111200-2000011-1-1-1-11100200-1-100000000
χ3222222-12-1222-1-1222-12-1-2-12-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-2111100220000-2-211-1-111-1-1-2-222-1-1-1-12002000011-1-111-1-100-2001100000000
χ332222-1222-122222-1-1-1-122-1-12-12-1-1-12220022-1-1-1-12-1-1-122-1-1-1-1-1-12202-1-1220000002222-1-100000002-1-1-1-1-1-10000-1-1-1-1000220000-1-10-100
χ342222-1222-122222-1-1-1-122-1-12-12-1-1-12220022-1-1-1-12-1-1-122-1-1-1-1-1-1-2-20211-2-20000002222-1-10000000-21-111110000-1-1-1-1000-2-20000110100
χ352222-1222-122222-1-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1220-2-1-122000000-2-2-2-21100000002-11-1-1-1-100001111000-2-20000110100
χ362222-1222-122222-1-1-1-122-1-12-12-1-1-122200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-20-211-2-2000000-2-2-2-2110000000-211111100001111000220000-1-10-100
χ372222-1222-122222-1-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-1-2111-2-21111112-20-2-1-1-2-200000022-2-2-1-10000000211-1-1110000-1-1110002-20000-1-10100
χ382222-1222-122222-1-1-1-12-2-1-12-12-1-1-12-2-20022-1-1-1-1-2111-2-2111111-220-2112200000022-2-2-1-10000000-2-1111-1-10000-1-111000-220000110-100
χ392222-1222-122222-1-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-1-2111-2-21111112-202-1-1-2-2000000-2-22211000000021-1-1-111000011-1-1000-220000110-100
χ402222-1222-122222-1-1-1-12-2-1-12-12-1-1-12-2-200-2-2-1-1-1-1-2111-2-2111111-22021122000000-2-222110000000-2-1-111-1-1000011-1-10002-20000-1-10100
χ412-22-2222-2-22-22-2-22-22220-2-2-222-22-2-2002i−2i2i−2i2-2-22000000000000000000002i−2i2i−2i002i−2i002i−2i2-222-2-2000000002i−2i002i−2i00000000000000000
χ422-22-2222-2-22-22-2-22-22220-2-2-222-22-2-2002i−2i−2i2i2-2-22000000000000000000002i−2i2i−2i00−2i2i00−2i2i-22-2-222000000002i−2i00−2i2i00000000000000000
χ432-22-2222-2-22-22-2-22-22220-2-2-222-22-2-200−2i2i2i−2i2-2-2200000000000000000000−2i2i−2i2i002i−2i002i−2i-22-2-22200000000−2i2i002i−2i00000000000000000
χ442-22-2222-2-22-22-2-22-22220-2-2-222-22-2-200−2i2i−2i2i2-2-2200000000000000000000−2i2i−2i2i00−2i2i00−2i2i2-222-2-200000000−2i2i00−2i2i00000000000000000
χ452-22-22-121-22-2-11-22-2-12-101-21-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i3000000002i−2i−ii3−3−ii3−32i−2i2-2-1-11100000000−ii3−3−ii3−300000−i3i300000000
χ462-22-22-121-22-2-11-22-2-12-101-21-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i3000000002i−2i−ii3−3i−i−33−2i2i-2211-1-100000000−ii3−3i−i−3300000i3−i300000000
χ472-22-22-121-22-2-11-22-2-12-101-21-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i300000000−2i2ii−i−33−ii3−32i−2i-2211-1-100000000i−i−33−ii3−300000i3−i300000000
χ482-22-22-121-22-2-11-22-2-12-101-21-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i300000000−2i2ii−i−33i−i−33−2i2i2-2-1-11100000000i−i−33i−i−3300000−i3i300000000
χ492-22-22-121-22-2-11-22-2-12-101-21-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i3000000002i−2i−ii−33−ii−332i−2i2-2-1-11100000000−ii−33−ii−3300000i3−i300000000
χ502-22-22-121-22-2-11-22-2-12-101-21-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i3000000002i−2i−ii−33i−i3−3−2i2i-2211-1-100000000−ii−33i−i3−300000−i3i300000000
χ512-22-22-121-22-2-11-22-2-12-101-21-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i300000000−2i2ii−i3−3−ii−332i−2i-2211-1-100000000i−i3−3−ii−3300000−i3i300000000
χ522-22-22-121-22-2-11-22-2-12-101-21-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i300000000−2i2ii−i3−3i−i3−3−2i2i2-2-1-11100000000i−i3−3i−i3−300000i3−i300000000
χ5344444-2-2-24-2-2-2-2-244-2-214-2-21-21-2-2-21-2-244001111-24-2-211-2-2111100400000-2-2-2-2-2-2000000000000-2000000011110000000000000000000
χ5444444-2-2-24-2-2-2-2-244-2-214-2-21-21-2-2-21-2-2-4-4001111-24-2-211-2-2111100-40000022222200000000000020000000-1-1-1-10000000000000000000
χ5544444-2-2-24-2-2-2-2-244-2-21-4-2-21-21-2-2-2122440011112-422-1-122-1-1-1-100-400000-2-2-2-2220000000000002000000011-1-10000000000000000000
χ5644444-2-2-24-2-2-2-2-244-2-21-4-2-21-21-2-2-2122-4-40011112-422-1-122-1-1-1-1004000002222-2-2000000000000-20000000-1-1110000000000000000000
χ574444-24-24-2-2-244-2-2-2-21-24-21-2-2-211-2-24400001111-2-2-2-2-2-21111114400-2-2-2-20000000000000000000-2-20111100000000000000000000000
χ584444-24-24-2-2-244-2-2-2-21-24-21-2-2-211-2-24400001111-2-2-2-2-2-2111111-4-40022220000000000000000000220-1-1-1-100000000000000000000000
χ594444-24-24-2-2-244-2-2-2-21-2-4-21-2-2-211-2-2-4-400001111222222-1-1-1-1-1-14-400-2-2220000000000000000000-22011-1-100000000000000000000000
χ604444-24-24-2-2-244-2-2-2-21-2-4-21-2-2-211-2-2-4-400001111222222-1-1-1-1-1-1-440022-2-200000000000000000002-20-1-11100000000000000000000000
χ614444-2-24-2-244-2-24-2-21-2-241-2-21-2-2-21-2-2-2004411114-211-2-2-2-2111100040000000000-2-2-2-2-2-2000000000-2000000001111000000000000000
χ624444-2-24-2-244-2-24-2-21-2-241-2-21-2-2-21-2-2-200-4-411114-211-2-2-2-21111000-40000000000222222000000000200000000-1-1-1-1000000000000000
χ634444-2-24-2-244-2-24-2-21-2-2-41-2-21-2-2-21-22200441111-42-1-12222-1-1-1-1000-40000000000-2-222-2-200000000020000000011-1-1000000000000000
χ644444-2-24-2-244-2-24-2-21-2-2-41-2-21-2-2-21-22200-4-41111-42-1-12222-1-1-1-10004000000000022-2-222000000000-200000000-1-111000000000000000
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χ7544-4-4-24-24-222-4-4-222-21-20-2-1-2221-12200000011-1-1000000−3i3i−3i3i−3i3i00002i3−2i323−230000000000000000000000−i3i3−3300000000000000000000000
χ764-44-444-2-4-4-224-424-44-2-20-4224-22-2-42004i−4i00-222-200000000000000000000−2i2i4i−4i0000000000000000000000−2i2i000000000000000000000
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χ784-44-44-2-22-4-22-2224-4-2-21022-1-212-22-1−2i32i34i−4i001-1-1100−2i32i3i3−i300i3i3−i3−i300000000−2i2i−2i2i23−2300000000000000000000i−i−330000000000000000000
χ794-44-44-2-22-4-22-2224-4-2-21022-1-212-22-1−2i32i3−4i4i001-1-1100−2i32i3i3−i300i3i3−i3−i3000000002i−2i2i−2i−232300000000000000000000−ii3−30000000000000000000
χ804-44-44-2-22-4-22-2224-4-2-21022-1-212-22-12i3−2i34i−4i001-1-11002i3−2i3−i3i300−i3−i3i3i300000000−2i2i−2i2i−232300000000000000000000i−i3−30000000000000000000
χ814-44-44-2-22-4-22-2224-4-2-21022-1-212-22-12i3−2i3−4i4i001-1-11002i3−2i3−i3i300−i3−i3i3i3000000002i−2i2i−2i23−2300000000000000000000−ii−330000000000000000000
χ824-44-4-244-424-44-4-4-22-2-24022-4-242-22-400004i−4i-222-2000000000000000000000000004i−4i00−2i2i000000000000000000−2i2i00000000000000000
χ834-44-4-244-424-44-4-4-22-2-24022-4-242-22-40000−4i4i-222-200000000000000000000000000−4i4i002i−2i0000000000000000002i−2i00000000000000000
χ844-44-4-2-24224-4-22-4-221-2-20-1221-22-2-12−2i32i3004i−4i1-1-1100i3−i3−2i32i300i3i3−i3−i300000000000000−2i2i23−23−2i2i000000000000000000i−i−33000000000000000
χ854-44-4-2-24224-4-22-4-221-2-20-1221-22-2-12−2i32i300−4i4i1-1-1100i3−i3−2i32i300i3i3−i3−i3000000000000002i−2i−23232i−2i000000000000000000−ii3−3000000000000000
χ864-44-4-2-24224-4-22-4-221-2-20-1221-22-2-122i3−2i3004i−4i1-1-1100−i3i32i3−2i300−i3−i3i3i300000000000000−2i2i−2323−2i2i000000000000000000i−i3−3000000000000000
χ874-44-4-2-24224-4-22-4-221-2-20-1221-22-2-122i3−2i300−4i4i1-1-1100−i3i32i3−2i300−i3−i3i3i3000000000000002i−2i23−232i−2i000000000000000000−ii−33000000000000000
χ884-4-44444-4-4-44-44-4-444440-44-4-4-4-4-4440000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-42-2-442-444-2-20-4-22-42224-2000000-22-22000000000000000000000000000000000000000000000000000000000000023−23000000
χ904-4-4444-2-4-42-2-442-444-2-20-4-22-42224-2000000-22-220000000000000000000000000000000000000000000000000000000000000−2323000000
χ914-4-444-242-4-442-2-4-44-24-2024222-4-4-2-2000000-22-220000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ924-4-444-242-4-442-2-4-44-24-2024222-4-4-2-2000000-22-2200000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ934-4-44-244-42-44-44-42-2-2-2402-2-42-422-24000000-22-2200000000000000000000000000000000000000000000000000000000000000023−230000
χ944-4-44-244-42-44-44-42-2-2-2402-2-42-422-24000000-22-22000000000000000000000000000000000000000000000000000000000000000−23230000
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
χ9788-8-88-4-4-484444-4-8-8-4-420-4424-2-444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-48-4-4-8-8448442-4-4024-4-24-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-44444-44422202-22-2-22-2-2-2000000-1-1110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4-44444-44422202-22-2-22-2-2-2000000-1-111000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4-84-448-84-44-42-404-24-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-444-44-444-442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-444-44-444-442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-44-84-44-44-88-4-4204-4-24-244-420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-844-4-8844-4-42-4042444-2-2-4-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-884-4-84-42-4-40-2-44-24442-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-44-444-42220-22-2-2-2-2-222000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-44-444-42220-22-2-2-2-2-222000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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