Finite Group Databasebeta

← Group #13167105

Character table — Group #13167105

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11112222222222444444444444444444444444444466666666666666666666666688888888889999121212121212121212121212121212121212121212121212181818181818181818183636363672727272108108108108
order12223446661212121233336666666666661212121212121212121212124444444412121212121212121212121212121212366612121212121222221212121212121212121212121212121212121212121212124466661212121222446612124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ911-1-11i−i1-1-1ii−i−i11111-1-1-1-1111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1i−iii−i−i1-11-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1011-1-11i−i1-1-1ii−i−i11111-1-1-1-1111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1i−iii−i−i1-11-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−i11-1-1ii−i−i-11−ii-11−ii-11−ii
χ1111-1-11i−i1-1-1ii−i−i11111-1-1-1-1111-1-1-1-1iiiiii−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1i−iii−i−i1-11-1-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−i11-1-1ii−i−i1-1i−i1-1i−i-11−ii
χ1211-1-11i−i1-1-1ii−i−i11111-1-1-1-1111-1-1-1-1iiiiii−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1i−iii−i−i1-11-1-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−i11-1-1ii−i−i-11−ii-11−ii1-1i−i
χ1311-1-11−ii1-1-1−i−iii11111-1-1-1-1111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−ii−i−iii1-11-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ1411-1-11−ii1-1-1−i−iii11111-1-1-1-1111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−ii−i−iii1-11-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii11-1-1−i−iii-11i−i-11i−i-11i−i
χ1511-1-11−ii1-1-1−i−iii11111-1-1-1-1111-1-1-1-1−i−i−i−i−i−iiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−ii−i−iii1-11-1-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii11-1-1−i−iii1-1−ii1-1−ii-11i−i
χ1611-1-11−ii1-1-1−i−iii11111-1-1-1-1111-1-1-1-1−i−i−i−i−i−iiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−ii−i−iii1-11-1-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii11-1-1−i−iii-11i−i-11i−i1-1−ii
χ172222222222222222222222222222222222222222220000000000000000000000002222222222-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2000000000000
χ1822222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2-2-2-2-200000000000000000000000022-2-2-2-22222000000000000
χ192222-122-1-1-1-1-1-1-12-1-1222-1-122-1-12-1-1222-1-1-1-122-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-1-1-122-1-1-1-1-2-2-2-200−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-211111111000000000000
χ202222-122-1-1-1-1-1-1-12-1-1222-1-122-1-12-1-1222-1-1-1-122-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-1-1-122-1-1-1-1-2-2-2-200i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-211111111000000000000
χ212222-122-1-1-1-1-1-1-12-1-1222-1-122-1-12-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ222222-122-1-1-1-1-1-1-12-1-1222-1-122-1-12-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-12222-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000
χ232222-1-2-2-1-1-111112-1-1222-1-122-1-12-1-12-2-21111-2-2111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-1-1-1-2-21111-2-2-2-200−i3−i3i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i3221111-1-1-1-1000000000000
χ242222-1-2-2-1-1-111112-1-1222-1-122-1-12-1-12-2-21111-2-2111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-1-1-1-2-21111-2-2-2-200i3i3−i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i3221111-1-1-1-1000000000000
χ252222-1-2-2-1-1-111112-1-1222-1-122-1-12-1-12-2-21111-2-211112222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-2-21111222222-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-1-1-1-11111000000000000
χ262222-1-2-2-1-1-111112-1-1222-1-122-1-12-1-12-2-21111-2-21111-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-2-211112222-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-1-1-1-11111000000000000
χ2722-2-222i−2i2-2-22i2i−2i−2i22222-2-2-2-2222-2-2-2-22i2i2i2i2i2i−2i−2i−2i−2i−2i−2i00000000000000000000000022-2-22i−2i2i2i−2i−2i-22-22000000000000000000000000−2i2i-2-222−2i−2i2i2i000000000000
χ2822-2-22−2i2i2-2-2−2i−2i2i2i22222-2-2-2-2222-2-2-2-2−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i00000000000000000000000022-2-2−2i2i−2i−2i2i2i-22-220000000000000000000000002i−2i-2-2222i2i−2i−2i000000000000
χ2922-2-2-12i−2i-111−i−iii2-1-122-211-22-1-1-211-22i2i−i−i−i−i−2i−2iiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333-1-1112i−2i−i−iii-22-2200−i3−i3i3i300i3i3−i3−i30033−3−300−3−333−2i2i11-1-1ii−i−i000000000000
χ3022-2-2-12i−2i-111−i−iii2-1-122-211-22-1-1-211-22i2i−i−i−i−i−2i−2iiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3-1-1112i−2i−i−iii-22-2200i3i3−i3−i300−i3−i3i3i300−3−3330033−3−3−2i2i11-1-1ii−i−i000000000000
χ3122-2-2-12i−2i-111−i−iii2-1-122-211-22-1-1-211-22i2i−i−i−i−i−2i−2iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii-1-1112i−2i−i−iii2-22-222-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i−2i-1-111−i−iii000000000000
χ3222-2-2-12i−2i-111−i−iii2-1-122-211-22-1-1-211-22i2i−i−i−i−i−2i−2iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i-1-1112i−2i−i−iii2-22-2-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i−2i-1-111−i−iii000000000000
χ3322-2-2-1−2i2i-111ii−i−i2-1-122-211-22-1-1-211-2−2i−2iiiii2i2i−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3-1-111−2i2iii−i−i-22-2200−i3−i3i3i300i3i3−i3−i300−3−3330033−3−32i−2i11-1-1−i−iii000000000000
χ3422-2-2-1−2i2i-111ii−i−i2-1-122-211-22-1-1-211-2−2i−2iiiii2i2i−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333-1-111−2i2iii−i−i-22-2200i3i3−i3−i300−i3−i3i3i30033−3−300−3−3332i−2i11-1-1−i−iii000000000000
χ3522-2-2-1−2i2i-111ii−i−i2-1-122-211-22-1-1-211-2−2i−2iiiii2i2i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i-1-111−2i2iii−i−i2-22-222-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i2i-1-111ii−i−i000000000000
χ3622-2-2-1−2i2i-111ii−i−i2-1-122-211-22-1-1-211-2−2i−2iiiii2i2i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii-1-111−2i2iii−i−i2-22-2-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i2i-1-111ii−i−i000000000000
χ372-22-2200-2-2200002222-22222-2-2-2-2-2-2-200000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-2-22000000-222-20000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i002-22-20000000000000000
χ382-22-2200-2-2200002222-22222-2-2-2-2-2-2-20000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-2-22000000-222-2000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i002-22-20000000000000000
χ392-22-2200-2-2200002222-22222-2-2-2-2-2-2-20000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000002-2-220000002-2-222i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000-22-220000000000000000
χ402-22-2200-2-2200002222-22222-2-2-2-2-2-2-2000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000002-2-220000002-2-22−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000-22-220000000000000000
χ412-22-2-10011-1−i3i3−i3i32-1-12-22-1-12-211-211-200−i3−i3i3i300−i3−i3i3i300002i−2i2i−2i3−3−333−3−33−ii−ii−ii−ii-111-100−i3i3−i3i3-222-2003−3−33003−3−332i−2i−ii−ii2i−2i−ii−ii00-11-11−i3i3−i3i3000000000000
χ422-22-2-10011-1−i3i3−i3i32-1-12-22-1-12-211-211-200−i3−i3i3i300−i3−i3i3i30000−2i2i−2i2i−333−3−333−3i−ii−ii−ii−i-111-100−i3i3−i3i3-222-200−333−300−333−3−2i2ii−ii−i−2i2ii−ii−i00-11-11−i3i3−i3i3000000000000
χ432-22-2-10011-1−i3i3−i3i32-1-12-22-1-12-211-211-200−i3−i3i3i300−i3−i3i3i32i−2i2i−2i0000−ii−ii−ii−ii3−3−333−3−33-111-100−i3i3−i3i32-2-222i−2i−ii−ii2i−2i−ii−ii003−3−33003−3−33001-11-1i3−i3i3−i3000000000000
χ442-22-2-10011-1−i3i3−i3i32-1-12-22-1-12-211-211-200−i3−i3i3i300−i3−i3i3i3−2i2i−2i2i0000i−ii−ii−ii−i−333−3−333−3-111-100−i3i3−i3i32-2-22−2i2ii−ii−i−2i2ii−ii−i00−333−300−333−3001-11-1i3−i3i3−i3000000000000
χ452-22-2-10011-1i3−i3i3−i32-1-12-22-1-12-211-211-200i3i3−i3−i300i3i3−i3−i300002i−2i2i−2i−333−3−333−3−ii−ii−ii−ii-111-100i3−i3i3−i3-222-200−333−300−333−32i−2i−ii−ii2i−2i−ii−ii00-11-11i3−i3i3−i3000000000000
χ462-22-2-10011-1i3−i3i3−i32-1-12-22-1-12-211-211-200i3i3−i3−i300i3i3−i3−i30000−2i2i−2i2i3−3−333−3−33i−ii−ii−ii−i-111-100i3−i3i3−i3-222-2003−3−33003−3−33−2i2ii−ii−i−2i2ii−ii−i00-11-11i3−i3i3−i3000000000000
χ472-22-2-10011-1i3−i3i3−i32-1-12-22-1-12-211-211-200i3i3−i3−i300i3i3−i3−i32i−2i2i−2i0000−ii−ii−ii−ii−333−3−333−3-111-100i3−i3i3−i32-2-222i−2i−ii−ii2i−2i−ii−ii00−333−300−333−3001-11-1−i3i3−i3i3000000000000
χ482-22-2-10011-1i3−i3i3−i32-1-12-22-1-12-211-211-200i3i3−i3−i300i3i3−i3−i3−2i2i−2i2i0000i−ii−ii−ii−i3−3−333−3−33-111-100i3−i3i3−i32-2-22−2i2ii−ii−i−2i2ii−ii−i003−3−33003−3−33001-11-1−i3i3−i3i3000000000000
χ492-2-22200-22-200002222-2-2-2-2-2-2-2-2222200000000000000002-2-22000000002-22-2-22-222-22-2000000-2-2220000000000002-22-22-2-22-22-22002-2-220000000000000000
χ502-2-22200-22-200002222-2-2-2-2-2-2-2-222220000000000000000-222-200000000-22-222-22-22-22-2000000-2-222000000000000-22-22-222-22-22-2002-2-220000000000000000
χ512-2-22200-22-200002222-2-2-2-2-2-2-2-222220000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000000002-22-200000022-2-22i−2i2i−2i2i−2i−2i2i−2i2i−2i2i00000000000000-222-20000000000000000
χ522-2-22200-22-200002222-2-2-2-2-2-2-2-22222000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000002-22-200000022-2-2−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i00000000000000-222-20000000000000000
χ532-2-22-1001-113−3−332-1-12-2-211-2-2112-1-120033−3−300−3−33300002-2-22−333−33−3−33-11-111-11-1-11-11003−3−33-2-22200−333−3003−3−332-2-11-11-221-11-100-111-13−3−33000000000000
χ542-2-22-1001-113−3−332-1-12-2-211-2-2112-1-120033−3−300−3−3330000-222-23−3−33−333−31-11-1-11-11-11-11003−3−33-2-222003−3−3300−333−3-221-11-12-2-11-1100-111-13−3−33000000000000
χ552-2-22-1001-113−3−332-1-12-2-211-2-2112-1-120033−3−300−3−3332i−2i−2i2i0000−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i3-11-11003−3−3322-2-22i−2i−ii−ii−2i2ii−ii−i00i3−i3−i3i300−i3i3i3−i3001-1-11−333−3000000000000
χ562-2-22-1001-113−3−332-1-12-2-211-2-2112-1-120033−3−300−3−333−2i2i2i−2i0000i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i3-11-11003−3−3322-2-2−2i2ii−ii−i2i−2i−ii−ii00−i3i3i3−i300i3−i3−i3i3001-1-11−333−3000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.