Finite Group Databasebeta

← Group #13178328

Character table — Group #13178328

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order1222333446666666663333344666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121244444444441212121222444441212121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-111-1-1-1-1-11-11
χ511111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11-111-1-11111-1-111-1-1-11-11
χ611111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-1-1-11-11-1-11111-1-11111-1-11-11-1
χ711111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111-1-11111-1-111-1-1-1-1
χ811111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11-11-1-11111-1-111-1-111-1-1111-1-11
χ101111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-111-1
χ111111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ121111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-11-1-11-1-1-1-1111111-1-1-1-111-1-1
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-1-1-1111111-111-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-11-1-1-111-1-111-1-111111-1-11
χ17222222-1222-122-122-122-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-12222222-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000022000000020002200-1-10000-1-100000-10-1
χ18222222-1222-122-122-122-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-12222222-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000-2-20000000-2000-2-2001100001100000101
χ19222222-1222-122-122-122-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21-21-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000000220000000-2000-2200-1-10000-1-100000101
χ20222222-1222-122-122-122-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21-21-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000000-2-2000000020002-2001100001100000-10-1
χ21222222-1-2-22-122-122-122-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-22-1-21-2-211111111-2-21111111122-1-1-1-1-1-1-1-10000002200000002000-2-200-1-100001100000-101
χ22222222-1-2-22-122-122-122-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-22-1-21-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000000-2-20000000-20002200110000-1-10000010-1
χ23222222-1-2-22-122-122-122-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-2-2-222-212-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000000220000000-20002-200-1-10000110000010-1
χ24222222-1-2-22-122-122-122-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-2-2-222-212-122-1-1-1-1-1-1-1-1-2-211111111-2-211111111000000-2-200000002000-2200110000-1-100000-101
χ2522222-1222-122-122-122-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-122222222-12-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000022000000002002200-1-10000-1-1000000-10-10
χ2622222-1222-122-122-122-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-122222222-12-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200000000-200-2-200110000110000001010
χ2722222-1222-122-122-122-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-12222-2-2-2-21-21-211-2-2111111-1-122-1-1-1-1-1-111-2-211111100002200000000-2002-200-1-10000-1-10000001010
χ2822222-1222-122-122-122-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-12222-2-2-2-21-21-211-2-2111111-1-122-1-1-1-1-1-111-2-21111110000-2-200000000200-220011000011000000-10-10
χ2922222-12-2-2-122-122-122-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-222-2-2-121-211-2-211111111-2-2111111-1-122-1-1-1-1-1-100002200000000200-2-200-1-1000011000000-1010
χ3022222-12-2-2-122-122-122-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-222-2-2-121-211-2-211111111-2-2111111-1-122-1-1-1-1-1-10000-2-200000000-2002200110000-1-100000010-10
χ3122222-12-2-2-122-122-122-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-2221-2-12-1-122-1-1-1-1-1-111-2-211111111-2-211111100002200000000-200-2200-1-100001100000010-10
χ3222222-12-2-2-122-122-122-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-2-2-2-2-2221-2-12-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-2000000002002-200110000-1-1000000-1010
χ332222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-12222-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222000022-1-1-1-100200000000-1-10000-1-1-1-10000
χ342222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-12222-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-20000-2-2111100-20000000011000011110000
χ352222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-12222-1-11111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111122220000-2-2111100-200000000-1-10000-1-1110000
χ362222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-12222-1-11111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111-2-2-2-2000022-1-1-1-10020000000011000011-1-10000
χ372222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-211-1-11122-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-122-2-20000-2-2111100200000000-1-1000011-1-10000
χ382222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-211-1-11122-2-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1-2-222000022-1-1-1-100-200000000110000-1-1110000
χ392222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-21111-1-1-2-222-1-1-1-122-1-1-1-11111-2-211111111-2-2111122-2-2000022-1-1-1-100-200000000-1-1000011110000
χ402222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-21111-1-1-2-222-1-1-1-122-1-1-1-11111-2-211111111-2-21111-2-2220000-2-2111100200000000110000-1-1-1-10000
χ412-22-22222i−2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002i−2i2-20000000000000000000002i−2i00002-2000000
χ422-22-22222i−2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000−2i2i-22000000000000000000000−2i2i0000-22000000
χ432-22-2222−2i2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002i−2i-220000000000000000000002i−2i0000-22000000
χ442-22-2222−2i2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000−2i2i2-2000000000000000000000−2i2i00002-2000000
χ452-22-2-1222i−2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i2i−2i−ii3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−32i−2i2-200000033−3−300000000000−ii0000-11−i3i30000
χ462-22-2-1222i−2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i2i−2i−ii3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−3−2i2i-22000000−3−33300000000000i−i00001-1i3−i30000
χ472-22-2-1222i−2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i2i−2i−ii−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−3332i−2i2-2000000−3−33300000000000−ii0000-11i3−i30000
χ482-22-2-1222i−2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-2112i−2i2i−2i−ii−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−333−2i2i-2200000033−3−300000000000i−i00001-1−i3i30000
χ492-22-2-122−2i2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2i−2i2ii−i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−32i−2i-22000000−3−33300000000000−ii00001-1−i3i30000
χ502-22-2-122−2i2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2i−2i2ii−i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−3−2i2i2-200000033−3−300000000000i−i0000-11i3−i30000
χ512-22-2-122−2i2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2i−2i2ii−i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−3332i−2i-2200000033−3−300000000000−ii00001-1i3−i30000
χ522-22-2-122−2i2i-2-21221-2-2-1-1-12-1-10011-211-1-12-1-111-211−2i2i−2i2ii−i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−333−2i2i2-2000000−3−33300000000000i−i0000-11−i3i30000
χ532-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2-22-22-200000002i−2i2i−2i00000000000000
χ542-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i-22-22-2200000002i−2i−2i2i00000000000000
χ552-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i-22-22-220000000−2i2i2i−2i00000000000000
χ562-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-22-20000000−2i2i−2i2i00000000000000
χ5744444-2-244-2-24-2-24-2-24-2-211144-2-2111-2-2111-2-2111-2-2-2-2444444-2-2-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
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χ6044444-2-2-4-4-2-24-2-24-2-24-2-2111-44-2-2111-2-2111-2-21112222-4-4-4-44422-2-2-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ614444-24-2444-2-24-2-24-2-2-21-21144-21-211-21-211-21-21144-2-2-2-2-2-2-2-24-24-2-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-2444-2-24-2-24-2-2-21-211-4-4-21-211-21-211-21-21144-2-2-2-22222-42-4222-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-44-2-24-2-24-2-2-21-2114-4-21-211-21-211-21-211-4-42222-2-2224-2-4222-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ644444-24-2-4-44-2-24-2-24-2-2-21-211-44-21-211-21-211-21-211-4-4222222-2-2-424-2-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ654444-2-2444-24-2-24-2-24-21-2-211441-2-2111-2-2111-2-211-2-244-2-2-2-2-2-2-24-2411-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-24-2-24-2-24-21-2-211-4-41-2-2111-2-2111-2-211-2-244-2-222222-42-4-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-24-2-24-2-24-21-2-2114-41-2-2111-2-2111-2-21122-4-422-2-222-242-4-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.