Finite Group Databasebeta

← Group #13178343

Character table — Group #13178343

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order12223334466666666633333446666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444412121212222444444466121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ611111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1-1111111111-1-1-1-111-1-1-1-1
χ711111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-11-1-111-1-1-1-111111111-1-1
χ811111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-111-1-111-1-11111-1-1-1-111
χ91111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111111-11-11-1-11-1111-1-1-1-1-1-111-1-1111-11-1
χ101111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111-11-111-11-11-1-1-11111-1-111-1-1-1-1-11-11
χ111111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-11-1-11-11111-1-111-1-111-1-11-1-11
χ121111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1111-11-1-1-1-11111-1-11111-111-1
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111-1-11-1111-1-1-1-11111-1-1-1-111-1-11-11-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-111-1-11-1-11111-1-1-1-1-1-1-1-11111-11-11
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1-1-11-11-111-1-1-1-1111111-1-1111-1-11
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-11111-1-11-1-11111-1-11111-1-1-1-1-111-1
χ17222222-122-12-122-12222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002220002000-1-100-1-100000000-1-100
χ18222222-122-12-122-12222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-122-1-1222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2000-2000110011000000001100
χ19222222-122-12-122-12222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-1-2-2-2-22211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111110000000022-2000-200011001100000000-1-100
χ20222222-122-12-122-12222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122-1-1-2-2-2-22211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-21111111100000000-2-220002000-1-100-1-1000000001100
χ21222222-1-2-2-12-122-12222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-21122-2-2-2-2-112-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111000000002-22000-2000-1-1001100000000-1100
χ22222222-1-2-2-12-122-12222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-21122-2-2-2-2-112-2-2-21111111122-1-1-1-1-1-1-1-1-2-21111111100000000-22-200020001100-1-1000000001-100
χ23222222-1-2-2-12-122-12222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-21-1-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-1000000002-2-200020001100-1-100000000-1100
χ24222222-1-2-2-12-122-12222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211-2-222-2-21-1-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-100000000-222000-2000-1-10011000000001-100
χ2522222-12222222-12-1-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-12222-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-10000220000000000-1-1-1-1-1-1000000
χ2622222-12222222-12-1-12-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-12222-1-1-1-1-1-12222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211110000-2-20000000000111111000000
χ2722222-12222222-12-1-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122221111-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-21111112222-1-1-1-10000-2-20000000000-1-11111000000
χ2822222-12222222-12-1-12-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122221111-1-1-2-2-2-2-1-122-1-1-1-1-1-111-2-211111111-2-2111111-2-2-2-21111000022000000000011-1-1-1-1000000
χ2922222-12-2-22222-12-1-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-1-111112-22-211-2-2111111-1-122-1-1-1-1-1-111-2-211111122-2-2-1-1-1-100002-2000000000011-1-111000000
χ3022222-12-2-22222-12-1-12-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-1-111112-22-211-2-2111111-1-122-1-1-1-1-1-111-2-2111111-2-22211110000-220000000000-1-111-1-1000000
χ3122222-12-2-22222-12-1-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-211-1-111-22-2211-2-211111111-2-2111111-1-122-1-1-1-1-1-122-2-2-1-1-1-10000-2200000000001111-1-1000000
χ3222222-12-2-22222-12-1-12-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-211-1-111-22-2211-2-211111111-2-2111111-1-122-1-1-1-1-1-1-2-222111100002-20000000000-1-1-1-111000000
χ332222-122222-12-12222-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-12222222222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000200022200-1-100000000-1-100-1-1
χ342222-122222-12-12222-1-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-12222222222-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000-2000-2-2-2001100000000110011
χ352222-122222-12-12222-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122-2-2-2-222-2-211-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000000002000-2-2200-1-100000000-1-10011
χ362222-122222-12-12222-1-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122-2-2-2-222-2-211-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000000-200022-20011000000001100-1-1
χ372222-122-2-22-12-12222-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-222-2-2-2-22-2-111111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000000002000-22-200-1-10000000011001-1
χ382222-122-2-22-12-12222-1-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-222-2-2-2-22-2-111111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000000-20002-22001100000000-1-100-11
χ392222-122-2-22-12-12222-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-222-2-2-221-11111-2-211111111-2-21111-1-1-1-122-1-1-1-10000000000020002-2-200-1-1000000001100-11
χ402222-122-2-22-12-12222-1-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-222-2-2-221-11111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000000-2000-222001100000000-1-1001-1
χ412-22-22222-2-22-2-2-22-22-22222200-2-2-2-2-222222-2-2-2-2-22-22-200002-200002-22-22-222-2-2000000000000000000002i−2i2i−2i2i2i−2i−2i00000000000000002i−2i0000000000
χ422-22-22222-2-22-2-2-22-22-22222200-2-2-2-2-222222-2-2-2-2-22-22-200002-200002-22-22-222-2-200000000000000000000−2i2i−2i2i−2i−2i2i2i0000000000000000−2i2i0000000000
χ432-22-2222-22-22-2-2-22-22-22222200-2-2-2-2-222222-2-2-2-2-2-22-220000-220000-22-22-22-2-222000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000000000−2i2i0000000000
χ442-22-2222-22-22-2-2-22-22-22222200-2-2-2-2-222222-2-2-2-2-2-22-220000-220000-22-22-22-2-22200000000000000000000−2i2i2i−2i−2i−2i2i2i00000000000000002i−2i0000000000
χ452-22-22-122-2-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-21112-22-23−33−3-110000-112-2-11-1-1113−3003−333−3−33−3003−333−3−32i−2i2i−2i−i−iii0000000000000000−ii−i3i3−i3i3000000
χ462-22-22-122-2-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-21112-22-23−33−3-110000-112-2-11-1-1113−3003−333−3−33−3003−333−3−3−2i2i−2i2iii−i−i0000000000000000i−ii3−i3i3−i3000000
χ472-22-22-122-2-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-21112-22-2−33−33-110000-112-2-11-1-111−3300−33−3−333−3300−33−3−3332i−2i2i−2i−i−iii0000000000000000−iii3−i3i3−i3000000
χ482-22-22-122-2-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-21112-22-2−33−33-110000-112-2-11-1-111−3300−33−3−333−3300−33−3−333−2i2i−2i2iii−i−i0000000000000000i−i−i3i3−i3i3000000
χ492-22-22-12-22-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-2111-22-223−3−331-100001-1-221-111-1-13−3003−333−3−3−3300−33−3−3332i−2i−2i2i−i−iii0000000000000000i−i−i3i3i3−i3000000
χ502-22-22-12-22-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-2111-22-223−3−331-100001-1-221-111-1-13−3003−333−3−3−3300−33−3−333−2i2i2i−2iii−i−i0000000000000000−iii3−i3−i3i3000000
χ512-22-22-12-22-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-2111-22-22−333−31-100001-1-221-111-1-1−3300−33−3−3333−3003−333−3−32i−2i−2i2i−i−iii0000000000000000i−ii3−i3−i3i3000000
χ522-22-22-12-22-22-2-2121-1-2-12-1-1-1001-2111-12-1-1-11-2111-22-22−333−31-100001-1-221-111-1-1−3300−33−3−3333−3003−333−3−3−2i2i2i−2iii−i−i0000000000000000−ii−i3i3i3−i3000000
χ5344444-2-244-24-24-2-2-2-24-2-211144-2-2111-2-2111-2-211144-2-2-2-2-2-2-2-2-2-244-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5444444-2-244-24-24-2-2-2-24-2-2111-4-4-2-2111-2-2111-2-211144-2-22222-2-222-4-4-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-2-2-4-4-24-24-2-2-2-24-2-21114-4-2-2111-2-2111-2-2111-4-422-2-22222-224-42222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-4-24-24-2-2-2-24-2-2111-44-2-2111-2-2111-2-2111-4-42222-2-2222-2-442222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ574444-24-244-2-2-2-24-244-2-21-21144-21-211-21-211-21-211-2-2-2-2444444-2-2-2-2-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ584444-24-244-2-2-2-24-244-2-21-211-4-4-21-211-21-211-21-211-2-2-2-2-4-4-4-4442222-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ594444-24-2-4-4-2-2-2-24-244-2-21-2114-4-21-211-21-211-21-211222244-4-4-4-4-22-2222-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ604444-24-2-4-4-2-2-2-24-244-2-21-211-44-21-211-21-211-21-2112222-4-444-4-42-22-222-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ614444-2-24444-24-2-24-2-2-21-2-211441-2-2111-2-2111-2-211-2-244-2-2-2-2-2-244-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ624444-2-24444-24-2-24-2-2-21-2-211-4-41-2-2111-2-2111-2-211-2-2442222-2-2-4-42211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ634444-2-24-4-44-24-2-24-2-2-21-2-2114-41-2-2111-2-2111-2-21122-4-4-2-222224-4-22-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ644444-2-24-4-44-24-2-24-2-2-21-2-211-441-2-2111-2-2111-2-21122-4-422-2-222-442-2-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ654444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i3244111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ664444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-4-4111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-22222-2-22222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
χ674444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i3244111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.