Finite Group Databasebeta

← Group #13178320

Character table — Group #13178320

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181818181818181836363636363636363636363636363636363636363672727272
order12223334466666666633333446666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212224444444412121212244444466661212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-11-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-11-11-1-1-111-1-1-1-1-1-1-1-1111-1-11
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-11-1-1-1-111-1-1-1-111-1-1-111-1
χ511111111111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-11-111111-1-111-1-1-1-111-111-1
χ611111111111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-11-111-1-11111-1-111-1-11-1-11
χ711111111111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ811111111111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-11-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ91111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-11-11
χ101111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1111111-1-1-1-11111-1-11-11-1
χ111111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111111111-1-1-11-1-11-1-1-1-1-1-111-1-11111-1-111
χ121111111-1-1111111111111111-1111111111111111-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111111-11-111-1-1-1111111-1-1-1-1-1-111-1-1
χ131111111-1-111111111111111-11111111111111111-1-1-1-111-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-111-1-1-1-1-1-1-1-1111111-1-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-111-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111-111-1-11111111-1-1-1-1-1-1-1-1-1-111
χ151111111-1-111111111111111-11111111111111111-1-1-1-111-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1111-11-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-111-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-111-1-1-1-111-1-1111111-1-1-11-11
χ17222222-1222-122-12-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222002200-1-1-1-10200000-1-10000-1-1-1-100000000
χ18222222-1222-122-12-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-20011110-200000110000111100000000
χ19222222-1222-122-12-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-1-1-111112222-2-2-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111222200-2-20011110-200000-1-10000-1-11100000000
χ20222222-1222-122-12-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-1-1-111112222-2-2-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-2002200-1-1-1-1020000011000011-1-100000000
χ21222222-1-2-22-122-12-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-111-1-111-2-2-2-2-22-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-2-200-2-20011110200000-1-1000011-1-100000000
χ22222222-1-2-22-122-12-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-111-1-111-2-2-2-2-22-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-222002200-1-1-1-10-200000110000-1-11100000000
χ23222222-1-2-22-122-12-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-11111-1-1-2-2-2-22-22-222-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-2-2002200-1-1-1-10-200000-1-10000111100000000
χ24222222-1-2-22-122-12-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-11111-1-1-2-2-2-22-22-222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-22200-2-20011110200000110000-1-1-1-100000000
χ2522222-1222-122-12222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122222222-1-1-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100002200000000200202000-1-100000000-1-1-100-1
χ2622222-1222-122-12222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122222222-1-1-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200000000-200-20-20001100000000111001
χ2722222-1222-122-12222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2-2-222-1-11-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-211111100002200000000200-20-2000-1-100000000-1-11001
χ2822222-1222-122-12222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2-2-222-1-11-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-21111110000-2-200000000-200202000110000000011-100-1
χ2922222-12-2-2-122-12222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-222-2-2-2-21112-2-111-2-211111111-2-2111111-1-122-1-1-1-1-1-100002200000000-20020-20001100000000-1-1100-1
χ3022222-12-2-2-122-12222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-222-2-2-2-21112-2-111-2-211111111-2-2111111-1-122-1-1-1-1-1-10000-2-200000000200-202000-1-10000000011-1001
χ3122222-12-2-2-122-12222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-222-2-211-1-221-1-122-1-1-1-1-1-111-2-211111111-2-211111100002200000000-200-2020001100000000-1-1-1001
χ3222222-12-2-2-122-12222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-222-2-211-1-221-1-122-1-1-1-1-1-111-2-211111111-2-21111110000-2-20000000020020-2000-1-10000000011100-1
χ332222-1222222-122-12-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1222222-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000022000000202020000-1-10000-1-1000-1-10
χ342222-1222222-122-12-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1222222-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2000000-20-20-2000011000011000110
χ352222-1222222-122-12-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-122-2-2-2-2-1-122-211-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000002200000020-20-20000-1-10000-1-1000110
χ362222-1222222-122-12-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-122-2-2-2-2-1-122-211-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000-2-2000000-20202000011000011000-1-10
χ372222-122-2-222-122-12-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-222-2-211-2-2-2-1121111-2-211111111-2-21111-1-1-1-122-1-1-1-10000000022000000-20-2020000110000-1-10001-10
χ382222-122-2-222-122-12-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-1-2-222-2-211-2-2-2-1121111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000-2-20000002020-20000-1-1000011000-110
χ392222-122-2-222-122-12-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-22211-2-221-1-2-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000022000000-2020-20000110000-1-1000-110
χ402222-122-2-222-122-12-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-2-2-22211-2-221-1-2-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000-2-200000020-2020000-1-10000110001-10
χ412-22-222200-22-2-2-22-2-222222200-2-2-2-2-2-2-2-2-2-2222220000000000000000000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i000000000000000002i−2i2-20000
χ422-22-222200-22-2-2-22-2-222222200-2-2-2-2-2-2-2-2-2-2222220000000000000000000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i00000000000000000−2i2i2-20000
χ432-22-222200-22-2-2-22-2-222222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i00000000000000000−2i2i-220000
χ442-22-222200-22-2-2-22-2-222222200-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i000000000000000002i−2i-220000
χ452-2-222222i−2i-2-2-222-2-22-22222200-2-2-2-2-222222-2-2-2-2-22i−2i00002i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i000000000000000002-200002i−2i0000000000
χ462-2-222222i−2i-2-2-222-2-22-22222200-2-2-2-2-222222-2-2-2-2-22i−2i00002i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i00000000000000000-220000−2i2i0000000000
χ472-2-22222−2i2i-2-2-222-2-22-22222200-2-2-2-2-222222-2-2-2-2-2−2i2i0000−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i000000000000000002-20000−2i2i0000000000
χ482-2-22222−2i2i-2-2-222-2-22-22222200-2-2-2-2-222222-2-2-2-2-2−2i2i0000−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i00000000000000000-2200002i−2i0000000000
χ492-2-2222-12i−2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111−ii3−3−i3i32i−2i2i−2i000000−i3i3−i3i3−i3−i3i3i32i−2i−ii−ii−i−iii003−33−333−3−32-22i−2i000000−i3i3−i3i30000000-110000−ii3−300000000
χ502-2-2222-12i−2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111−ii3−3−i3i32i−2i2i−2i000000−i3i3−i3i3−i3−i3i3i32i−2i−ii−ii−i−iii003−33−333−3−3-22−2i2i000000i3−i3i3−i300000001-10000i−i−3300000000
χ512-2-2222-12i−2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111−ii−33i3−i32i−2i2i−2i000000i3−i3i3−i3i3i3−i3−i32i−2i−ii−ii−i−iii00−33−33−3−3332-22i−2i000000i3−i3i3−i30000000-110000−ii−3300000000
χ522-2-2222-12i−2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111−ii−33i3−i32i−2i2i−2i000000i3−i3i3−i3i3i3−i3−i32i−2i−ii−ii−i−iii00−33−33−3−333-22−2i2i000000−i3i3−i3i300000001-10000i−i3−300000000
χ532-2-2222-1−2i2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111i−i3−3i3−i3−2i2i−2i2i000000i3−i3i3−i3i3i3−i3−i3−2i2ii−ii−iii−i−i003−33−333−3−32-2−2i2i000000i3−i3i3−i30000000-110000i−i3−300000000
χ542-2-2222-1−2i2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111i−i3−3i3−i3−2i2i−2i2i000000i3−i3i3−i3i3i3−i3−i3−2i2ii−ii−iii−i−i003−33−333−3−3-222i−2i000000−i3i3−i3i300000001-10000−ii−3300000000
χ552-2-2222-1−2i2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111i−i−33−i3i3−2i2i−2i2i000000−i3i3−i3i3−i3−i3i3i3−2i2ii−ii−iii−i−i00−33−33−3−3332-2−2i2i000000−i3i3−i3i30000000-110000i−i−3300000000
χ562-2-2222-1−2i2i-21-22-1-212-22-1-1-1-100-211112-1-1-1-1-21111i−i−33−i3i3−2i2i−2i2i000000−i3i3−i3i3−i3−i3i3i3−2i2ii−ii−iii−i−i00−33−33−3−333-222i−2i000000i3−i3i3−i300000001-10000−ii3−300000000
χ5744444-2-244-2-24-2-24-24-2-2-211144-2-2111-2-2111-2-2111-2-2-2-2-2-244-2-2-244-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000000
χ5844444-2-244-2-24-2-24-24-2-2-2111-4-4-2-2111-2-2111-2-2111-2-2222244-2-22-4-422222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000000
χ5944444-2-2-4-4-2-24-2-24-24-2-2-21114-4-2-2111-2-2111-2-211122-2-222-4-42224-4-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000000
χ6044444-2-2-4-4-2-24-2-24-24-2-2-2111-44-2-2111-2-2111-2-21112222-2-2-4-422-2-442-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000000
χ614444-24-2444-2-24-2-2-2-24-21-21144-21-211-21-211-21-211-2-2-2-2-2-2-2-2444-2-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000000
χ624444-24-2444-2-24-2-2-2-24-21-211-4-4-21-211-21-211-21-211-2-22222-2-244-422-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000000
χ634444-24-2-4-44-2-24-2-2-2-24-21-2114-4-21-211-21-211-21-21122-2-22222-4-4-4-22422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000000
χ644444-24-2-4-44-2-24-2-2-2-24-21-211-44-21-211-21-211-21-2112222-2-222-4-442-2-4-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000000
χ654444-2-2444-24-2-24-24-2-21-2-211441-2-2111-2-2111-2-211444444-2-2-2-2-2-2-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000000
χ664444-2-2444-24-2-24-24-2-21-2-211-4-41-2-2111-2-2111-2-21144-4-4-4-4-2-2-2-22222-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000000
χ674444-2-24-4-4-24-2-24-24-2-21-2-2114-41-2-2111-2-2111-2-211-4-444-4-422222-22-2-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000000
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χ1114-4-44-2-2-2−4i4i222-2-222-22111−1−3i32−1+3i3200-1-1-11+3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i322i−2i−2323−2i32i32i−2i2i−2i00003-3i3−i3i3−i3−3−i323−i323+i32−3+i32−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11−3i3i3−33−3−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000000000000000000000
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χ1238-88-8-4-4-4004-4444-444-4222−1+3i3−1−3i300-2-2-21−3i31+3i3-2-2-21−3i31+3i3222−1+3i3−1−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000

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