Finite Group Databasebeta

← Group #13178322

Character table — Group #13178322

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order122233344666666666333334466666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212122244444444121212122444444661212121212121212121212126121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-111-11-11
χ511111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-11-111-1-11111-1-111-1-1-11-11
χ611111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-11-1-111111-1-111-1-1-1-1111-11-1
χ711111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1111-1-1-11111-1-1111111-1-1-1-1
χ811111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-11-11-1-1-1-1-1-1-1-111-1-1-1-11111
χ91111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11-1111-1-111-1-111-1-111-1-1111-1-11
χ101111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-11-1-11111111-1-1-1-11111-1-1-111-1
χ111111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ121111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-111-111-1-1-1-1-1-111-1-11111-1-111
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-11-1-1-11111111-1-1-1-1-1-1-1-1-1-111
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-11-111-1-1-1-1-1-1-1-1111111-1-1
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-111-11-1-1-1-1111111-1-111-111-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-111-1-1111111-1-11-1-11
χ17222222-1222-122-122-122-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000220000000020000220000-1-10000-1-100-10-10
χ18222222-1222-122-122-122-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-200000000-20000-2-2000011000011001010
χ19222222-1222-122-122-122-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-1-2-2-2-22211-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-21111111100002200000000-200002-20000-1-10000-1-1001010
χ20222222-1222-122-122-122-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-1-2-2-2-22211-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-2111111110000-2-20000000020000-2200001100001100-10-10
χ21222222-1-2-22-122-122-122-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-21122-2-2-2-2-112-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-10000220000000020000-2-20000-1-100001100-1010
χ22222222-1-2-22-122-122-122-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-21122-2-2-2-2-112-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-10000-2-200000000-20000220000110000-1-10010-10
χ23222222-1-2-22-122-122-122-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-21-1-2222-1-1-1-1-1-1-1-1-2-211111111-2-21111111100002200000000-20000-220000-1-10000110010-10
χ24222222-1-2-22-122-122-122-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-21-1-2222-1-1-1-1-1-1-1-1-2-211111111-2-2111111110000-2-200000000200002-20000110000-1-100-1010
χ2522222-1222-122-122-122-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12222002200-1-1-1-10000200-1-10000-1-1-1-100000000
χ2622222-1222-122-122-122-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200-2-20011110000-200110000111100000000
χ2722222-1222-122-122-122-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-122111122-2-2-2-211-2-2111111-1-122-1-1-1-1-1-111-2-211111122-2-200220011110000-200-1-10000-1-11100000000
χ2822222-1222-122-122-122-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-1-122111122-2-2-2-211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-2-22200-2-200-1-1-1-1000020011000011-1-100000000
χ2922222-12-2-2-122-122-122-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-1-111-2-22-22-211-2-211111111-2-2111111-1-122-1-1-1-1-1-122-2-200-2-20011110000200-1-1000011-1-100000000
χ3022222-12-2-2-122-122-122-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-111-2-2-1-111-2-22-22-211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-2-222002200-1-1-1-10000-200110000-1-11100000000
χ3122222-12-2-2-122-122-122-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-211-1-1-2-2-22-22-1-122-1-1-1-1-1-111-2-211111111-2-2111111222200-2-200-1-1-1-10000-200-1-10000111100000000
χ3222222-12-2-2-122-122-122-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-111-2-211-1-1-2-2-22-22-1-122-1-1-1-1-1-111-2-211111111-2-2111111-2-2-2-200220011110000200110000-1-1-1-100000000
χ332222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122222222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000220000022200000-1-100000000-1-10-10-1
χ342222-1222222-122-122-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122222222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-200000-2-2-2000001100000000110101
χ352222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-12222-2-2-2-2-1-1-2-2111111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000002200000-2-2200000-1-100000000-1-10101
χ362222-1222222-122-122-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-12222-2-2-2-2-1-1-2-2111111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000-2-20000022-2000001100000000110-10-1
χ372222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-222-2-2112-2-111111-2-211111111-2-21111-1-1-1-122-1-1-1-10000000022000002-2-200000-1-100000000110-101
χ382222-122-2-222-122-122-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-222-2-2112-2-111111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000-2-200000-222000001100000000-1-1010-1
χ392222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-2-2-22211-221-1-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000002200000-22-200000-1-10000000011010-1
χ402222-122-2-222-122-122-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-2-2-22211-221-1-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000-2-2000002-22000001100000000-1-10-101
χ412-22-22222i−2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i00002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-200002i−2i00000000000002-200002i−2i0000000000
χ422-22-22222i−2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-22i−2i2i−2i00002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-220000−2i2i0000000000000-220000−2i2i0000000000
χ432-22-2222−2i2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i0000−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-20000−2i2i00000000000002-20000−2i2i0000000000
χ442-22-2222−2i2i-2-2-222-2-2-222222200-2-2-2-2-222222-2-2-2-2-2−2i2i−2i2i0000−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-2200002i−2i0000000000000-2200002i−2i0000000000
χ452-22-22-122i−2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111−ii2i−2i3−3−i3i32i−2i0000−i3i300−i3i3−i3−i3i3i3−ii2i−2i−ii−i−iii3−3003−333−3−32-200002i−2i00−i3−i3i3i30000000-110000−ii3−300000000
χ462-22-22-122i−2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111−ii2i−2i3−3−i3i32i−2i0000−i3i300−i3i3−i3−i3i3i3−ii2i−2i−ii−i−iii3−3003−333−3−3-220000−2i2i00i3i3−i3−i300000001-10000i−i−3300000000
χ472-22-22-122i−2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111−ii2i−2i−33i3−i32i−2i0000i3−i300i3−i3i3i3−i3−i3−ii2i−2i−ii−i−iii−3300−33−3−3332-200002i−2i00i3i3−i3−i30000000-110000−ii−3300000000
χ482-22-22-122i−2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111−ii2i−2i−33i3−i32i−2i0000i3−i300i3−i3i3i3−i3−i3−ii2i−2i−ii−i−iii−3300−33−3−333-220000−2i2i00−i3−i3i3i300000001-10000i−i3−300000000
χ492-22-22-12−2i2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111i−i−2i2i3−3i3−i3−2i2i0000i3−i300i3−i3i3i3−i3−i3i−i−2i2ii−iii−i−i3−3003−333−3−32-20000−2i2i00i3i3−i3−i30000000-110000i−i3−300000000
χ502-22-22-12−2i2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111i−i−2i2i3−3i3−i3−2i2i0000i3−i300i3−i3i3i3−i3−i3i−i−2i2ii−iii−i−i3−3003−333−3−3-2200002i−2i00−i3−i3i3i300000001-10000−ii−3300000000
χ512-22-22-12−2i2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111i−i−2i2i−33−i3i3−2i2i0000−i3i300−i3i3−i3−i3i3i3i−i−2i2ii−iii−i−i−3300−33−3−3332-20000−2i2i00−i3−i3i3i30000000-110000i−i−3300000000
χ522-22-22-12−2i2i1-2-2-12-21-22-12-1-1-1001-2111-12-1-1-11-2111i−i−2i2i−33−i3i3−2i2i0000−i3i300−i3i3−i3−i3i3i3i−i−2i2ii−iii−i−i−3300−33−3−333-2200002i−2i00i3i3−i3−i300000001-10000−ii3−300000000
χ532-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i2i−2i002-22i−2i2i−2i0000000002-22i−2i000000000000
χ542-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i−2i2i00-222i−2i2i−2i000000000-22−2i2i000000000000
χ552-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i2i−2i00-22−2i2i−2i2i000000000-222i−2i000000000000
χ562-2-2222200-2-22-2-2-222-2222220022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i−2i2i002-2−2i2i−2i2i0000000002-2−2i2i000000000000
χ5744444-2-244-2-24-2-24-2-24-2-211144-2-2111-2-2111-2-2111-2-2-2-2-2-2-2-244-2-244-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-2-24-2-24-2-24-2-2111-4-4-2-2111-2-2111-2-2111-2-2-2-222224422-4-42222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-2-24-2-24-2-24-2-21114-4-2-2111-2-2111-2-21112222-2-222-4-4-224-42222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ6044444-2-2-4-4-2-24-2-24-2-24-2-2111-44-2-2111-2-2111-2-2111222222-2-2-4-42-2-44-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ614444-24-2444-2-24-2-24-2-2-21-21144-21-211-21-211-21-21144-2-24444-2-2-2-2-2-2-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-2444-2-24-2-24-2-2-21-211-4-4-21-211-21-211-21-21144-2-2-4-4-4-4-2-2222222-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-44-2-24-2-24-2-2-21-2114-4-21-211-21-211-21-211-4-42244-4-422-22-2222-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ644444-24-2-4-44-2-24-2-24-2-2-21-211-44-21-211-21-211-21-211-4-422-4-444222-22-2-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ654444-2-2444-24-2-24-2-24-21-2-211441-2-2111-2-2111-2-211-2-244-2-2-2-2-2-244-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-24-2-24-2-24-21-2-211-4-41-2-2111-2-2111-2-211-2-2442222-2-2-4-422-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-24-2-24-2-24-21-2-2114-41-2-2111-2-2111-2-21122-4-4-2-222224-4-22-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
χ684444-2-24-4-4-24-2-24-2-24-21-2-211-441-2-2111-2-2111-2-21122-4-422-2-222-442-211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.