Finite Group Databasebeta

← Group #13168587

Character table — Group #13168587

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order12223336666666663334666666666121212121212121244444412121212366612121212121212121224466121212121212121212121212121212121212121244446661212121212121212124444121212121212441212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-1-1-111111111111111111111-1-111-1-1-1-11-1-1-111111-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-11111111-1-1-1-111-1-111111111-1-1-1-11111-1111-1-1-1-1-11-11-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-11-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-1-11-111-1-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-11-1-1-1-1-1-1111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-11-1-1-1-1-1111111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-111
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-11-111111-1-1-111-1-1-111-1-11111-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1111-111-1-1-1-11111-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-11111-1-111-1-111-1-11-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1111-1-1-1-1-111-1-111-1-111-1-111111-1-1-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11-111111-1-11-111-1-1-1-111-1-1-1111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111-11-1-1-1-1-111-111-1-1-111-1-1-1-111-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-111111-1-111-1-11-1
χ17222222-122-122-1-1222-1-122-12-1-1-1-1-12-1-122-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-120222-1-1220000-1-100-1-1-1-1-1-1-1-10000-1-1-1-102-1-10000020200000000-10-10
χ18222222-122-122-1-1222-1-122-12-1-1-1-1-12-1-122-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-1-20-2-2-2-1-1220000-1-100-1-1-1-1-1-1-1-1000011110-21100000-20-2000000001010
χ19222222-122-122-1-1222-1-122-12-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-12022211-2-200001100111111110000-1-1-1-102-1-100000-20-2000000001010
χ20222222-122-122-1-1222-1-122-12-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-2-211-2-20000110011111111000011110-2110000020200000000-10-10
χ21222222-122-122-1-1222-1-1-22-12-1-1-1-1-1211-2-211112200-2-2-2-2-2-2-1-1-1-1-2-2-211111120-222-1-12200001100-1-1-1-111110000-1-1-110-21100000-2020000000010-10
χ22222222-122-122-1-1222-1-1-22-12-1-1-1-1-1211-2-211112200-2-2-2-2-2-2-1-1-1-1-2-2-2111111-202-2-2-1-12200001100-1-1-1-111110000111-102-1-10000020-200000000-1010
χ23222222-122-122-1-1222-1-1-22-12-1-1-1-1-1211-2-21111-2-200222222-1-1-1-1-2-2-211111120-22211-2-20000-1-1001111-1-1-1-10000-1-1-110-2110000020-200000000-1010
χ24222222-122-122-1-1222-1-1-22-12-1-1-1-1-1211-2-21111-2-200222222-1-1-1-1-2-2-2111111-202-2-211-2-20000-1-1001111-1-1-1-10000111-102-1-100000-2020000000010-10
χ2522222-12-1222-122-12-12-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-10000222200-1-10000000022002-1-12-1-1-1-1-1-1-1-10020-1-10000000-100
χ2622222-12-1222-122-12-12-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2110000222200-1-100000000-2-200-211-2-1111-1-1-1-100-20110000000100
χ2722222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-12-22-1-10000-2-2-2-2001100000000-2-2002-1-121-1-1-1111100-20110000000100
χ2822222-12-1222-122-12-12-12-1-1-12-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2110000-2-2-2-20011000000002200-211-2111111110020-1-10000000-100
χ2922222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-2-1-1000022-2-200-1-10000000022002-1-1-21111-1-11100-20-1-10000000100
χ3022222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-2-2211000022-2-200-1-100000000-2-200-21121-1-1-1-1-1110020110000000-100
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χ3222222-12-1222-122-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-222110000-2-2220011000000002200-2112-1-1-1-111-1-100-20-1-10000000100
χ332222-1222-12-12222-1-1-122-12-1-12-1-12-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-10200022-1-1-1-1-1-12222-1-1-1-1-1-1-1-1002200002000-1-1-1-1200000-1-1-1-1000000
χ342222-1222-12-12222-1-1-122-12-1-12-1-12-122-1-1-1-1-1-122-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-10-200022-1-1111122-2-2-1-1-1-1-1-1-1-100-2-20000-20001111-2000001111000000
χ352222-1222-12-12222-1-1-122-12-1-12-1-12-122-1-1-1-1-1-1-2-222-2-21111-1-1-1-12-1-122-1-1-1-102000-2-211-1-1-1-1-2-2221111111100-2-200002000-1-1-1-1-2000001111000000
χ362222-1222-12-12222-1-1-122-12-1-12-1-12-122-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-10-2000-2-2111111-2-2-2-21111111100220000-20001111200000-1-1-1-1000000
χ372222-1222-12-12222-1-1-12-2-12-1-12-1-12-1-2-21111112222-2-21111-1-1-1-1-211-2-211110-200022-1-1-1-111-2-222-1-1-1-1111100220000-2000-1-111-200000-1-111000000
χ382222-1222-12-12222-1-1-12-2-12-1-12-1-12-1-2-211111122-2-2-2-21111-1-1-1-1-211-2-211110200022-1-111-1-1-2-2-2-2-1-1-1-1111100-2-20000200011-1-120000011-1-1000000
χ392222-1222-12-12222-1-1-12-2-12-1-12-1-12-1-2-2111111-2-22222-1-1-1-1-1-1-1-1-211-2-211110-2000-2-211-1-11122221111-1-1-1-100-2-20000-2000-1-11120000011-1-1000000
χ402222-1222-12-12222-1-1-12-2-12-1-12-1-12-1-2-2111111-2-2-2-222-1-1-1-1-1-1-1-1-211-2-2111102000-2-21111-1-122-2-21111-1-1-1-100220000200011-1-1-200000-1-111000000
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χ502-22-2-122-21-2122-2-2-1-1-1201-2-1-1211-2100−i3i3−i3−i3i3i32i−2i−2i2i003−33−3-111-10−i3i300−i3−i3i3i3000002i−2i−iii−i−3300−2i2i−i−iii3−33−300-2200000000i−i−330000001-1i3−i3000000
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χ934-4-4444-2442-4-42-2-4-44-2-204-2-4222-22-4−232300−232323−230000000000-22-22000−2323−232323−23000000000000000000000000000000000000000000000000000000000
χ944-4-444-24-24-4-42-442-4-24-20-2-22-42-4422000000000000000000-22-22000000000000−2i32i30000000000000000000000000−2i32i30000000000000000000000000
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χ1004-4-44-2444-2-42-4-44-42-2-240-2422-42-2-4200000000000000−2i32i32i3−2i3-22-22000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
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χ1024-4-44-24-24-222-42-2-42-21-20-2-22-12-112223−2300−333−3000000−2i32i32i3−2i31-11-100023−23−333−3000000000000000003i−3i−3i3ii3−i3−i3i300000000000000000000000000000000
χ1034-4-44-24-24-222-42-2-42-21-20-2-22-12-112223−2300−333−30000002i3−2i3−2i32i31-11-100023−23−333−300000000000000000−3i3i3i−3i−i3i3i3−i300000000000000000000000000000000
χ1044-4-44-24-24-222-42-2-42-21-20-2-22-12-1122−2323003−3−33000000−2i32i32i3−2i31-11-1000−23233−3−3300000000000000000−3i3i3i−3ii3−i3−i3i300000000000000000000000000000000
χ1054-4-44-24-24-222-42-2-42-21-20-2-22-12-1122−2323003−3−330000002i3−2i3−2i32i31-11-1000−23233−3−33000000000000000003i−3i−3i3i−i3i3i3−i300000000000000000000000000000000
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χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
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χ11188-8-8-4-4-444-4-4444-442220-2-2-2-2-22-2220000−6i6i−6i6i0000000000-1-111000003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1128-88-88-4-44-84-8-4-4448-4-4204-2-4-4244-240000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-44444-4-444-42220-2-2222-2-2-2-200−4i34i32i32i3−2i3−2i30000000000-111-102i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-44444-4-444-42220-2-2222-2-2-2-2004i3−4i3−2i3−2i32i32i30000000000-111-10−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
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χ1168-8-88-4-4-4-4-44444-444222022-2-2-2-22-2-243−4300−232323−230000000000-11-11000−23233−3−33000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-4-44444-444222022-2-2-2-22-2-2−43430023−23−23230000000000-11-1100023−23−333−3000000000000000000000000000000000000000000000000000000000

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