Finite Group Databasebeta

← Group #13178209

Character table — Group #13178209

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order122233344666666666233333466666666666666666121212121212121266666666666612121212121212121212121212121212121212121212444444444412121212222444466121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-11111-1-1-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-111-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1111-1-11
χ5111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-11-111-1-111-1-11111-1-11-1-11
χ6111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-11-1-11-11-1-11111-1-1-1-11111-111-1
χ7111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-11-1-111111-1-11111-1-111-1-1-1-1
χ8111111111111111111-111111-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111111-1-11111-1-1
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1-1111-111111111-1-1-1-1-1-1-1-111
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1-1-11-1-1-111-1-1-1-11111-1-1-11-11
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-11-11-1111-1-1-1-1-1-1-1-111111-11-1
χ131111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-111111111-1-11-11-1-1-1-11111-1-111-1-1-1-11-11-1
χ141111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1111111-1-1-11111-1-111-1-1-1-1-1-111-11-11
χ151111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111
χ161111111-1-1111111111-1111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-11111-1-1-11111-1-111-1-111-1-111-1-1
χ17222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1002200000000002200200-1-1000000-1-100000-1-10
χ18222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-20000000000-2-200-200110000001100000110
χ19222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-2111111111-222-1-1-1-1-1-1-1-1-2-211111111002200000000002-200-200-1-1000000-1-100000110
χ20222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-21-2-2111111111-222-1-1-1-1-1-1-1-1-2-21111111100-2-20000000000-2200200110000001100000-1-10
χ21222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-11-2-2-211111111-2-21111111100220000000000-2200-20011000000-1-100000-110
χ22222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-11-2-2-211111111-2-21111111100-2-200000000002-200200-1-100000011000001-10
χ23222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-211111111-12-2-21111111122-1-1-1-1-1-1-1-100220000000000-2-20020011000000-1-1000001-10
χ24222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21122-21-2-211111111-12-2-21111111122-1-1-1-1-1-1-1-100-2-200000000002200-200-1-10000001100000-110
χ2522222-12222-1-122222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1222222-12-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000220000002002200-1-100000000-1-1-100-1
χ2622222-12222-1-122222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1222222-12-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2000000-200-2-2001100000000111001
χ2722222-12222-1-122222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-21-211-2-2111111-21-1-122-1-1-1-1-1-111-2-21111110000000022000000-200-2200-1-100000000-1-11001
χ2822222-12222-1-122222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-21-211-2-2111111-21-1-122-1-1-1-1-1-111-2-211111100000000-2-20000002002-200110000000011-100-1
χ2922222-12-2-22-1-122222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-2111-2-211111111-2-21111110000000022000000-2002-200-1-10000000011100-1
χ3022222-12-2-22-1-122222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-2111-2-211111111-2-211111100000000-2-2000000200-22001100000000-1-1-1001
χ3122222-12-2-22-1-122222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2221-211-2-21111112-111-2-2111111-1-122-1-1-1-1-1-10000000022000000200-2-200-1-10000000011-1001
χ3222222-12-2-22-1-122222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2221-211-2-21111112-111-2-2111111-1-122-1-1-1-1-1-100000000-2-2000000-20022001100000000-1-1100-1
χ332222-12222222-1-122-122-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12200222200-1-1-1-100020000000-1-1-1-100-1-1000000
χ342222-12222222-1-122-122-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-2001111000-2000000011110011000000
χ352222-12222222-1-122-12-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-122-1-12211-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-21111220022-2-2001111000-20000000-1-11100-1-1000000
χ362222-12222222-1-122-12-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-122-1-12211-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-200-2-22200-1-1-1-10002000000011-1-10011000000
χ372222-122-2-2222-1-122-122-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-211112200-2-2-2-200111100020000000-1-1-1-10011000000
χ382222-122-2-2222-1-122-122-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-21111-2-200222200-1-1-1-1000-20000000111100-1-1000000
χ392222-122-2-2222-1-122-12-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-1-1-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-12200-2-22200-1-1-1-1000-20000000-1-1110011000000
χ402222-122-2-2222-1-122-12-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-1-1-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-1-2-20022-2-20011110002000000011-1-100-1-1000000
χ4122-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002-2002i−2i2i−2i2i2i−2i−2i0000000002i−2i00002-200000000
χ4222-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002-200−2i2i−2i2i−2i−2i2i2i000000000−2i2i00002-200000000
χ4322-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000-22002i−2i−2i2i2i2i−2i−2i000000000−2i2i0000-2200000000
χ4422-2-222200-22-22-22-2-2-2022222000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000-2200−2i2i2i−2i−2i−2i2i2i0000000002i−2i0000-2200000000
χ452-22-22222i−2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002i−2i002-200000000000000000002i−2i00002-2000000
χ462-22-22222i−2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000−2i2i00-220000000000000000000−2i2i0000-22000000
χ472-22-2222−2i2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002i−2i00-2200000000000000000002i−2i0000-22000000
χ482-22-2222−2i2i2-22-2-2-2-22-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000−2i2i002-20000000000000000000−2i2i00002-2000000
χ492-22-2-1222i−2i2-2211-2-2-1-20-1-12-1-10−i3i3-1-12-1-11111-2-211112i−2i−ii2i−2i3−300−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−32i−2i002-20000−i3i3−i3i300000000000−ii3−300-11000000
χ502-22-2-1222i−2i2-2211-2-2-1-20-1-12-1-10−i3i3-1-12-1-11111-2-211112i−2i−ii2i−2i3−300−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−3−2i2i00-220000i3−i3i3−i300000000000i−i−33001-1000000
χ512-22-2-1222i−2i2-2211-2-2-1-20-1-12-1-10i3−i3-1-12-1-11111-2-211112i−2i−ii2i−2i−3300i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−3332i−2i002-20000i3−i3i3−i300000000000−ii−3300-11000000
χ522-22-2-1222i−2i2-2211-2-2-1-20-1-12-1-10i3−i3-1-12-1-11111-2-211112i−2i−ii2i−2i−3300i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−333−2i2i00-220000−i3i3−i3i300000000000i−i3−3001-1000000
χ532-22-2-122−2i2i2-2211-2-2-1-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−2i2ii−i−2i2i−3300−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−3332i−2i00-220000i3−i3i3−i300000000000−ii3−3001-1000000
χ542-22-2-122−2i2i2-2211-2-2-1-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−2i2ii−i−2i2i−3300−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−333−2i2i002-20000−i3i3−i3i300000000000i−i−3300-11000000
χ552-22-2-122−2i2i2-2211-2-2-1-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−2i2ii−i−2i2i3−300i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−32i−2i00-220000−i3i3−i3i300000000000−ii−33001-1000000
χ562-22-2-122−2i2i2-2211-2-2-1-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−2i2ii−i−2i2i3−300i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−3−2i2i002-20000i3−i3i3−i300000000000i−i3−300-11000000
χ5744444-2-244-2-2-244-2-24-24-2-2111444-2-2111-2-2-2-2111111-2-244-2-244-2-2-2-2-2-2111111-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-2-2-244-2-24-2-4-2-2111-4-4-4-2-2111-2-2-2-2111111-2-244-2-2-4-4222222-1-1-1-1-1-122-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-2-2-244-2-24-24-2-2111-444-2-2111-2-2-2-211111122-4-422-4-4-2-2-2-2-2-2111111222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ6044444-2-2-4-4-2-2-244-2-24-2-4-2-21114-4-4-2-2111-2-2-2-211111122-4-42244222222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ614444-24-244-244-2-2-2-2-244-21-2114-2-2-21-211-2-211-2-2111144-2-2-2-2-2-24-2-2-211-2-21111-24-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-244-244-2-2-2-2-24-4-21-211-422-21-211-2-211-2-2111144-2-2-2-222-4222-1-122-1-1-1-12-4-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-4-244-2-2-2-2-244-21-211-4-2-2-21-211-2-211-2-21111-4-42222224-2-2-211-2-211112-422-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ644444-24-2-4-4-244-2-2-2-2-24-4-21-211422-21-211-2-211-2-21111-4-42222-2-2-4222-1-122-1-1-1-1-2422-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ654444-2-24444-2-2-2-244-2-241-2-2114-2-21-2-21111-2-2-2-21111-2-2-2-244-2-2-2411-2-2-2-211114-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-24444-2-2-2-244-2-2-41-2-211-4221-2-21111-2-2-2-21111-2-2-2-244222-4-1-12222-1-1-1-1-4211-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-44-2-2-2-244-2-241-2-211-4-2-21-2-21111-2-2-2-211112222-4-422-2411-2-2-2-21111-42-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
χ684444-2-24-4-44-2-2-2-244-2-2-41-2-2114221-2-21111-2-2-2-211112222-4-4-2-22-4-1-12222-1-1-1-14-2-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
χ694444-2-2-244-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000000
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χ1054-44-4-2-2-2−4i4i-22-22222-220111−1+3i32−1−3i320−2i32i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i−232300i3−i3i3−i3-333−i32−3−i32−3+i323+i3200−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ113−33−33i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000000000000000000
χ1064-44-4-2-2-2−4i4i-22-22222-220111−1+3i32−1−3i3202i3−2i3111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i322i−2i2i−2i2i−2i23−2300−i3i3−i3i33-3−3+i323+i323−i32−3−i3200−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000000000000000000
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χ1228-8-88-4-4-4004444-44-44-40222−1−3i3−1+3i3000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1238-8-88-4-4-4004444-44-44-40222−1+3i3−1−3i3000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.