Finite Group Databasebeta

← Group #13178326

Character table — Group #13178326

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order122233344666666666333334466666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212122244444444121212122444444661212121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-11-1-111-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-11-1111111-1-111-1-111-1-1-1-1
χ611111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1111-1-11111-1-111-1-1-1-111
χ711111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1111111-1-1
χ91111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1111111111-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-11
χ101111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11-11-111-11111-1-11111-1-1-1-11-11-1
χ111111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-11111-1-1-1-11111-1-1-1-111-1-1-111-1
χ121111111-1-1111111111111111-1111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-11-11-111-1-1-1-1111111-1-111-11-11
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-11-1-11-1-111-1-1-1-111-1-1-1-111-111-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-11-11
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1111111-1-1-1-1-1-11-1-11
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1-111-1-11111111-11-1
χ17222222-122-122-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220000000000002202000-1-100-1-100000000-1-100
χ18222222-122-122-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-12222-12-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2000000000000-2-20-2000110011000000001100
χ19222222-122-122-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-2-2-2-21-21-2-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122000000000000-2-202000-1-100-1-1000000001100
χ20222222-122-122-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-2-2-2-21-21-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-2000000000000220-200011001100000000-1-100
χ21222222-1-2-2-122-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-21122-2-212-1-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-1220000000000002-20-2000-1-1001100000000-1100
χ22222222-1-2-2-122-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-21122-2-212-1-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-2000000000000-22020001100-1-1000000001-100
χ23222222-1-2-2-122-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-222-1-21222-1-1-1-1-1-1-1-1-2-211111111-2-21111111122000000000000-220-2000-1-10011000000001-100
χ24222222-1-2-2-122-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-2-222-1-21222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-20000000000002-2020001100-1-100000000-1100
χ2522222-122222-122-122-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122-1-12222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000220000002020200-1-100000000-1-100-1-1
χ2622222-122222-122-122-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122-1-12222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2000000-20-20-2001100000000110011
χ2722222-122222-122-122-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-1-122-2-2-2-2-21-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111000000002200000020-20-200-1-100000000-1-10011
χ2822222-122222-122-122-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-1-122-2-2-2-2-21-2111-2-2111111-1-122-1-1-1-1-1-111-2-211111100000000-2-2000000-202020011000000001100-1-1
χ2922222-12-2-222-122-122-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-222-2-2-2-12111-2-211111111-2-2111111-1-122-1-1-1-1-1-10000000022000000-20-202001100000000-1-1001-1
χ3022222-12-2-222-122-122-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-222-2-2-2-12111-2-211111111-2-2111111-1-122-1-1-1-1-1-100000000-2-20000002020-200-1-1000000001100-11
χ3122222-12-2-222-122-122-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-2-2-22221-2-1-1-122-1-1-1-1-1-111-2-211111111-2-21111110000000022000000-2020-2001100000000-1-100-11
χ3222222-12-2-222-122-122-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-2-2-22221-2-1-1-122-1-1-1-1-1-111-2-211111111-2-211111100000000-2-200000020-20200-1-10000000011001-1
χ332222-122222-122-122-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022222200-1-1-1-10000020000000-1-1-1-1-1-1000000
χ342222-122222-122-122-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-2-2-200111100000-20000000111111000000
χ352222-122222-122-122-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122221111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-211110022-2-2-2-200-1-1-1-1000002000000011-1-111000000
χ362222-122222-122-122-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122221111-2-2-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100-2-2222200111100000-20000000-1-111-1-1000000
χ372222-122-2-22-122-122-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-2-1-111-222-21111-2-211111111-2-21111-1-1-1-122-1-1-1-10022-2-22200-1-1-1-100000-200000001111-1-1000000
χ382222-122-2-22-122-122-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-2-1-111-222-21111-2-211111111-2-21111-1-1-1-122-1-1-1-100-2-222-2-20011110000020000000-1-1-1-111000000
χ392222-122-2-22-122-122-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-211-1-12-2-22-1-1-1-122-1-1-1-11111-2-211111111-2-21111002222-2-200-1-1-1-100000-20000000-1-11111000000
χ402222-122-2-22-122-122-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-211-1-12-2-22-1-1-1-122-1-1-1-11111-2-211111111-2-2111100-2-2-2-222001111000002000000011-1-1-1-1000000
χ412-22-222200-2-2-2-2222-2-22222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000002-22i−2i00002i−2i2i2i−2i−2i00000002-200000000002i−2i0000
χ422-22-222200-2-2-2-2222-2-22222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000002-2−2i2i0000−2i2i−2i−2i2i2i00000002-20000000000−2i2i0000
χ432-22-222200-2-2-2-2222-2-22222200-2-2-2-2-2-2-2-2-2-22222200000000000000000000000000000000000000000000-222i−2i0000−2i2i2i2i−2i−2i0000000-220000000000−2i2i0000
χ442-22-222200-2-2-2-2222-2-22222200-2-2-2-2-2-2-2-2-2-22222200000000000000000000000000000000000000000000-22−2i2i00002i−2i−2i−2i2i2i0000000-2200000000002i−2i0000
χ452-2-222222i−2i2-2-2-2-2-2-2222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i000000000000002i−2i2-200000000000000000002i−2i002-2000000
χ462-2-222222i−2i2-2-2-2-2-2-2222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000000000−2i2i-220000000000000000000−2i2i00-22000000
χ472-2-22222−2i2i2-2-2-2-2-2-2222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i000000000000002i−2i-2200000000000000000002i−2i00-22000000
χ482-2-22222−2i2i2-2-2-2-2-2-2222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000000000−2i2i2-20000000000000000000−2i2i002-2000000
χ492-2-22-1222i−2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211−ii2i−2i2i−2i3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−300002i−2i2-2003−33−30000000000000−ii−i3i3-11000000
χ502-2-22-1222i−2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211−ii2i−2i2i−2i3−3−i3i30000−i3i3−i3i300−i3−i3i3i3−ii−ii2i−2i−i−iii3−33−30033−3−30000−2i2i-2200−33−330000000000000i−ii3−i31-1000000
χ512-2-22-1222i−2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211−ii2i−2i2i−2i−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−33300002i−2i2-200−33−330000000000000−iii3−i3-11000000
χ522-2-22-1222i−2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211−ii2i−2i2i−2i−33i3−i30000i3−i3i3−i300i3i3−i3−i3−ii−ii2i−2i−i−iii−33−3300−3−3330000−2i2i-22003−33−30000000000000i−i−i3i31-1000000
χ532-2-22-122−2i2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211i−i−2i2i−2i2i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−300002i−2i-2200−33−330000000000000−ii−i3i31-1000000
χ542-2-22-122−2i2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211i−i−2i2i−2i2i3−3i3−i30000i3−i3i3−i300i3i3−i3−i3i−ii−i−2i2iii−i−i3−33−30033−3−30000−2i2i2-2003−33−30000000000000i−ii3−i3-11000000
χ552-2-22-122−2i2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211i−i−2i2i−2i2i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−33300002i−2i-22003−33−30000000000000−iii3−i31-1000000
χ562-2-22-122−2i2i21-2-21-2-2-12-1-12-1-10011-211-1-12-1-111-211i−i−2i2i−2i2i−33−i3i30000−i3i3−i3i300−i3−i3i3i3i−ii−i−2i2iii−i−i−33−3300−3−3330000−2i2i2-200−33−330000000000000i−i−i3i3-11000000
χ5744444-2-244-24-2-24-2-24-2-2-211144-2-2111-2-2111-2-211144-2-2-2-24444-2-2-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-24-2-24-2-24-2-2-2111-4-4-2-2111-2-2111-2-211144-2-2-2-2-4-4-4-422222222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-24-2-24-2-24-2-2-21114-4-2-2111-2-2111-2-2111-4-4222244-4-42-2-222222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ6044444-2-2-4-4-24-2-24-2-24-2-2-2111-44-2-2111-2-2111-2-2111-4-42222-4-444-222-2-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ614444-24-244-2-24-2-24-2-24-21-21144-21-211-21-211-21-211-2-244-2-2-2-2-2-2-24-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-244-2-24-2-24-2-24-21-211-4-4-21-211-21-211-21-211-2-244-2-222222-42-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-4-2-24-2-24-2-24-21-2114-4-21-211-21-211-21-21122-4-422-2-22224-2-422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ644444-24-2-4-4-2-24-2-24-2-24-21-211-44-21-211-21-211-21-21122-4-42222-2-2-2-424-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ654444-2-24444-2-24-2-24-2-21-2-211441-2-2111-2-2111-2-211-2-2-2-244-2-2-2-24-24-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-24444-2-24-2-24-2-21-2-211-4-41-2-2111-2-2111-2-211-2-2-2-2442222-42-42-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-44-2-24-2-24-2-21-2-2114-41-2-2111-2-2111-2-2112222-4-4-2-222-4-242-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.