Finite Group Databasebeta

← Group #13169181

Character table — Group #13169181

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121244441212121212121212121212121212121222224444666612121212121212121212121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-11111111111-1-111-1-111-1-1-1-1111111-11-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-11111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111-111111111-1-1-1-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1111
χ51111111111111111111111111111111-1-11111111111111111111-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11-1111111-1-1-1-11111-1111-1-1-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1-111-1-1-11-1-11111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11-111-1-111-1-111-1-11-111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1111111-1-111111-1-11-1-11111-1-1-1-111-1-11111-1-1-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-11111111111-1-11111-111-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-11-1-111-1-111-1-1111-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-111-11-1-11111-11-11
χ17222222-12-1222-1-1222-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1022022-1-1-1-1-1-1-1-100220022000022-1-1-1-102020000-1-1-1-1-1-1-1-1000000-1-10000
χ18222222-12-1222-1-1222-1-122-1-1-1-122-1-1-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-102-2022-1-1-1-1111100-2-200-2-20000-2-21111020-20000-1-1-1-11111000000110000
χ19222222-12-1222-1-1222-1-122-1-1-1-122-1-1-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-10-220-2-21111-1-1-1-1002200-2-20000-2-211110-20200001111-1-1-1-1000000110000
χ20222222-12-1222-1-1222-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-10-2-20-2-21111111100-2-20022000022-1-1-1-10-20-2000011111111000000-1-10000
χ21222222-12-1222-1-1222-1-1-22-1-1-1-122-1-1112222-1-1-1-1-2-21111-2-211110-2-2022-1-111-1-111002200-2-200002211110-20-20000-1-111-1-111000000-1-10000
χ22222222-12-1222-1-1222-1-1-22-1-1-1-122-1-11122-2-2-1-1-1-1-2-21111-2-211110-22022-1-11111-1-100-2-200220000-2-2-1-1-1-10-2020000-1-11111-1-1000000110000
χ23222222-12-1222-1-1222-1-1-22-1-1-1-122-1-111-2-222-1-1-1-1-2-21111-2-2111102-20-2-211-1-1-1-111002200220000-2-2-1-1-1-1020-2000011-1-1-1-111000000110000
χ24222222-12-1222-1-1222-1-1-22-1-1-1-122-1-111-2-2-2-2-1-1-1-1-2-21111-2-211110220-2-211-1-111-1-100-2-200-2-200002211110202000011-1-111-1-1000000-1-10000
χ2522222-12-12-122222-1-12-12-12-12-1-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-12022000000222222-1-1-1-1002200000000-102-1-1-1-1-10000-1-1-1-102-1-100000-100
χ2622222-12-12-122222-1-12-12-12-12-1-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-1-202-20000002222-2-2-1-11100-2-20000000010-2-111110000-1-1-1-10-21100000100
χ2722222-12-12-122222-1-12-12-12-12-1-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-120-22000000-2-2-2-22211-1-100-2-200000000-1021-1-1-1-1000011110-21100000100
χ2822222-12-12-122222-1-12-12-12-12-1-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-20-2-2000000-2-2-2-2-2-2111100220000000010-2111110000111102-1-100000-100
χ2922222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-11-2-2-21111111120-2-200000022-2-222-1-11100-2-200000000-10-2111-1-10000-1-111021100000-100
χ3022222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-20022-1-1-1-11-2-2-211111111-20-2200000022-2-2-2-2-1-1-1-10022000000001021-1-1110000-1-1110-2-1-100000100
χ3122222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-11-2-2-211111111202-2000000-2-222221111002200000000-10-2-111-1-1000011-1-10-2-1-100000100
χ3222222-12-12-122222-1-12-1-2-12-12-1-1-12-1-2-200-2-2-1-1-1-11-2-2-211111111-2022000000-2-222-2-211-1-100-2-200000000102-1-1-111000011-1-1021100000-100
χ332222-122222-1-122-12-1-122-1-12-12-1-1-12222200-1-1-1-12-1-1-122-1-1-1-1-1-12202-1-122220000-1-100220000220000002-1-10-1-1-1-1-1-1-1-100002000-1-100-1000
χ342222-122222-1-122-12-1-122-1-12-12-1-1-12222200-1-1-1-12-1-1-122-1-1-1-1-1-1-220-2-1-1222200001100-2-20000-2-2000000-2-1101111-1-1-1-10000-200011001000
χ352222-122222-1-122-12-1-122-1-12-12-1-1-1222-2-200-1-1-1-12-1-1-122-1-1-1-1-1-12-20211-2-2-2-20000-1-100220000-2-200000021-10-1-1-1-111110000-200011001000
χ362222-122222-1-122-12-1-122-1-12-12-1-1-1222-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-2-20-211-2-2-2-200001100-2-2000022000000-21101111111100002000-1-100-1000
χ372222-122222-1-122-12-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-1-2111-2-21111112-20-2-1-122-2-20000-1-100-2-2000022000000211011-1-1-1-1110000-2000-1-1001000
χ382222-122222-1-122-12-1-12-2-1-12-12-1-1-12-2-22200-1-1-1-1-2111-2-2111111-2-202-1-122-2-200001100220000-2-2000000-21-10-1-111-1-111000020001100-1000
χ392222-122222-1-122-12-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-1-2111-2-2111111220-211-2-2220000-1-100-2-20000-2-20000002-11011-1-111-1-1000020001100-1000
χ402222-122222-1-122-12-1-12-2-1-12-12-1-1-12-2-2-2-200-1-1-1-1-2111-2-2111111-220211-2-2220000110022000022000000-2-1-10-1-11111-1-10000-2000-1-1001000
χ4122-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200000022-2-2000000000000000000000000000000002-22-22-20022-2-20000000000000000002-22-2000000
χ4222-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200000022-2-2000000000000000000000000000000002-2-22-220022-2-2000000000000000000-22-22000000
χ4322-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200000022-2-200000000000000000000000000000000-222-2-2200-2-2220000000000000000002-2-22000000
χ4422-2-222222-22-2-2-2-2-22220222-2-2-2-2-2-200000022-2-200000000000000000000000000000000-22-222-200-2-222000000000000000000-222-2000000
χ452-22-2222-2-22-2-22-22-22220-2-2-222-22-2-2002i−2i2i−2i2-2-2200000000000000002i−2i2i−2i002i−2i00002i−2i000000002-20000000000002i−2i002i−2i000000002-20000
χ462-22-2222-2-22-2-22-22-22220-2-2-222-22-2-2002i−2i−2i2i2-2-2200000000000000002i−2i2i−2i00−2i2i0000−2i2i00000000-220000000000002i−2i00−2i2i00000000-220000
χ472-22-2222-2-22-2-22-22-22220-2-2-222-22-2-200−2i2i2i−2i2-2-220000000000000000−2i2i−2i2i002i−2i00002i−2i00000000-22000000000000−2i2i002i−2i00000000-220000
χ482-22-2222-2-22-2-22-22-22220-2-2-222-22-2-200−2i2i−2i2i2-2-220000000000000000−2i2i−2i2i00−2i2i0000−2i2i000000002-2000000000000−2i2i00−2i2i000000002-20000
χ492-22-222-1-212-2-2-112-22-1-10-211-1-1-2211−i3i32i−2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i300002i−2i−ii3−3−ii3−3002i−2i000000002-2−i3i3−i3i300000000−ii3−3−ii3−3000000-110000
χ502-22-222-1-212-2-2-112-22-1-10-211-1-1-2211−i3i32i−2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i300002i−2i−ii3−3i−i−3300−2i2i00000000-22i3−i3i3−i300000000−ii3−3i−i−330000001-10000
χ512-22-222-1-212-2-2-112-22-1-10-211-1-1-2211−i3i3−2i2i2i−2i-111-100−i3i3−i3i300−i3−i3i3i30000−2i2ii−i−33−ii3−3002i−2i00000000-22i3−i3i3−i300000000i−i−33−ii3−30000001-10000
χ522-22-222-1-212-2-2-112-22-1-10-211-1-1-2211−i3i3−2i2i−2i2i-111-100−i3i3−i3i300−i3−i3i3i30000−2i2ii−i−33i−i−3300−2i2i000000002-2−i3i3−i3i300000000i−i−33i−i−33000000-110000
χ532-22-222-1-212-2-2-112-22-1-10-211-1-1-2211i3−i32i−2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i300002i−2i−ii−33−ii−33002i−2i000000002-2i3−i3i3−i300000000−ii−33−ii−33000000-110000
χ542-22-222-1-212-2-2-112-22-1-10-211-1-1-2211i3−i32i−2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i300002i−2i−ii−33i−i3−300−2i2i00000000-22−i3i3−i3i300000000−ii−33i−i3−30000001-10000
χ552-22-222-1-212-2-2-112-22-1-10-211-1-1-2211i3−i3−2i2i2i−2i-111-100i3−i3i3−i300i3i3−i3−i30000−2i2ii−i3−3−ii−33002i−2i00000000-22−i3i3−i3i300000000i−i3−3−ii−330000001-10000
χ562-22-222-1-212-2-2-112-22-1-10-211-1-1-2211i3−i3−2i2i−2i2i-111-100i3−i3i3−i300i3i3−i3−i30000−2i2ii−i3−3i−i3−300−2i2i000000002-2i3−i3i3−i300000000i−i3−3i−i3−3000000-110000
χ5744444-2-2-2-2-244-2-24-2-2-214-2-21-21-2-2-21-2-200441111-24-2-211-2-211110040000000-2-2-2-200-2-200000000000000000-2000000001111000000000000
χ5844444-2-2-2-2-244-2-24-2-2-214-2-21-21-2-2-21-2-200-4-41111-24-2-211-2-2111100-400000002222002200000000000000000200000000-1-1-1-1000000000000
χ5944444-2-2-2-2-244-2-24-2-2-21-4-2-21-21-2-2-2122004411112-422-1-122-1-1-1-100-40000000-2-22200-2-20000000000000000020000000011-1-1000000000000
χ6044444-2-2-2-2-244-2-24-2-2-21-4-2-21-21-2-2-212200-4-411112-422-1-122-1-1-1-1004000000022-2-2002200000000000000000-200000000-1-111000000000000
χ614444-24-24-24-2-2-2-2-24-21-24-21-21-2-2-21-2-2-2440011114-211-2-2-2-211110400-2-2-2-2-2-200000000000000000000000-200000011110000000000000000
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χ804-44-44-2-222-2-4-4-2242-2-21022-1-212-22-12i3−2i300−4i4i1-1-11002i3−2i3−i3i300−i3−i3i3i300000000002i−2i23−23002i−2i00000000000000000000000000−ii−33000000000000
χ814-44-4-244-4-44224-4-2-4-2-24022-4-242-22-4004i−4i00-222-20000000000000000−2i2i4i−4i00000000000000000000000000000000−2i2i000000000000000000
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χ834-44-4-24-2-42422-22-2-4-21-202-121-22-2-12−2i32i34i−4i001-1-1100i3−i3−2i32i300i3i3−i3−i30000−2i2i−2i2i23−23000000000000000000000000000000i−i−330000000000000000
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χ864-44-4-24-2-42422-22-2-4-21-202-121-22-2-122i3−2i3−4i4i001-1-1100−i3i32i3−2i300−i3−i3i3i300002i−2i2i−2i23−23000000000000000000000000000000−ii−330000000000000000
χ874-4-44444-4-4-4-44-44-444440-4-4-4-4-44-4440000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-2-42-4-442-2-444-2-20-422224-4-2-2000000-22-220000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ894-4-4444-2-42-4-442-2-444-2-20-422224-4-2-2000000-22-2200000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ904-4-444-242-42-44-44-4-2-24-202-42-42-224-2000000-22-22000000000000000000000000000000−2i32i30000000000000000−2i32i30000000000000000000000
χ914-4-444-242-42-44-44-4-2-24-202-42-42-224-2000000-22-220000000000000000000000000000002i3−2i300000000000000002i3−2i30000000000000000000000
χ924-4-44-244-4-4-42-2-4424-2-24022-42-4-22-24000000-22-220000000000000000000000000023−23000000000000000000000023−2300000000000000000000
χ934-4-44-244-4-4-42-2-4424-2-24022-42-4-22-24000000-22-2200000000000000000000000000−23230000000000000000000000−232300000000000000000000
χ944-4-44-2-242-422-2-442-21-2-20-122221-1-2-20000001-11-10000003i−3i3i−3i3i−3i0000000000000023−2300−2i32i30000000000000000i3−i3−3300000000000000000000
χ954-4-44-2-242-422-2-442-21-2-20-122221-1-2-20000001-11-10000003i−3i3i−3i3i−3i00000000000000−2323002i3−2i30000000000000000−i3i33−300000000000000000000
χ964-4-44-2-242-422-2-442-21-2-20-122221-1-2-20000001-11-1000000−3i3i−3i3i−3i3i0000000000000023−23002i3−2i30000000000000000−i3i3−3300000000000000000000
χ974-4-44-2-242-422-2-442-21-2-20-122221-1-2-20000001-11-1000000−3i3i−3i3i−3i3i00000000000000−232300−2i32i30000000000000000i3−i33−300000000000000000000
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
χ10088-8-88-4-4-4-448-844-84-4-420-4-424-2444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-48-4-8-44444-8-42-40-42-4-2444-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-484-44-8-8442-4-402-4-444-2-24400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-4-44-4444442220222-2-2-2-2-2-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-484-8-4448-8-442-4-40-244-4-4-22440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-444-44-442220-2-2-222-22-2-2−4i34i30000-111-1002i3−2i32i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-444-44-442220-2-2-222-22-2-24i3−4i30000-111-100−2i32i3−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-4444-884-4-8-4-4-42044-24-2-44-420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-84-84-44-448-42-404-24-24-442-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44444-44-44-42220-2-2-2-2-22-222000000-11-110000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44444-44-44-42220-2-2-2-2-22-222000000-11-11000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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