Finite Group Databasebeta

← Group #72253917

Character table — Group #72253917

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111122222222224444444444444444444444444488888888888888888888888888888888161616161616161616161616161616161616161616161616242424244848484848484848484848484848
order1222223444466622222244444466666612121212121212126666888888881212121224242424242424242424242424242424224444446666121212121212121212121212444422444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11-1-11-11-11-1ii−i−iii−i−i
χ101111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-111-11-11-11−i−iii−i−iii
χ111111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii-1-111-1-111−i−i−i−iiiii11-1-1-111-1-11ii−i−i−i−iii
χ121111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii-1-111-1-111−i−i−i−iiiii-1-1111-1-111-1−i−iiiii−i−i
χ131111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii11-1-111-1-1−i−i−i−iiiii11-1-11-11-11-1−i−iii−i−iii
χ141111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii11-1-111-1-1−i−i−i−iiiii-1-111-11-11-11ii−i−iii−i−i
χ151111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i-1-111-1-111iiii−i−i−i−i11-1-1-111-1-11−i−iiiii−i−i
χ161111111-1-1-1-1111-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i-1-111-1-111iiii−i−i−i−i-1-1111-1-111-1ii−i−i−i−iii
χ17222222222222222-2-22-2-222-2-2-2-222222222222222-2-2-2-200000000-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000000000
χ18222222222222222-2-22-2-222-2-2-2-222222222222222-2-2-2-200000000-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000000000
χ1922222222222222-22-2-22-2-2-222-2-22-2-22-2-2-2-2-2-2222222-2-20000000022-2-2000000000000000000000000000000000000000000002200-2-200000000
χ2022222222222222-22-2-22-2-2-222-2-22-2-22-2-2-2-2-2-2222222-2-20000000022-2-200000000000000000000000000000000000000000000-2-2002200000000
χ2122222222222222-2-22-2-22-2-2-2-2222-2-22-2-2-2-2-2-22222-2-22200000000-2-2220000000000000000000000000000000000000000222200-2-20000000000
χ2222222222222222-2-22-2-22-2-2-2-2222-2-22-2-2-2-2-2-22222-2-22200000000-2-2220000000000000000000000000000000000000000-2-2-2-200220000000000
χ232222222-2-2-2-222222-222-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-200000000-2-222000000000000000000000000000000000000000022-2-200-220000000000
χ242222222-2-2-2-222222-222-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-200000000-2-2220000000000000000000000000000000000000000-2-222002-20000000000
χ252222222-2-2-2-22222-222-22-2-222-2-2222222-2-2-2-2-2-2-2-2-2-2220000000022-2-2000000000000000000000000000000000000000000002-200-2200000000
χ262222222-2-2-2-22222-222-22-2-222-2-2222222-2-2-2-2-2-2-2-2-2-2220000000022-2-200000000000000000000000000000000000000000000-22002-200000000
χ272222222-2-2-2-2222-222-22222-2-2-2-22-2-22-2-22222-2-2-2-2222200000000-2-2-2-200000000000000002-2-22000022-2-2-2-22200000000000000000000000000
χ282222222-2-2-2-2222-222-22222-2-2-2-22-2-22-2-22222-2-2-2-2222200000000-2-2-2-20000000000000000-222-20000-2-22222-2-200000000000000000000000000
χ29222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ30222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ31222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000
χ32222222-12222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000
χ33222222-12222-1-1-12-2-22-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-20000-1-1-1-11111−i3−i3i3i3−i3−i3i3i3000000000000000000
χ34222222-12222-1-1-12-2-22-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-22200001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ35222222-12222-1-1-12-2-22-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-20000-1-1-1-11111i3i3−i3−i3i3i3−i3−i3000000000000000000
χ36222222-12222-1-1-12-2-22-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-22200001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000
χ37222222-1-2-2-2-2-1-1-1-222-22222-2-2-2-2-111-111-1-1-1-11111-1-1-1-10000000011113333−3−3−3−3−3−3−3−333332-2-220000-1-11111-1-133−3−3−3−333000000000000000000
χ38222222-1-2-2-2-2-1-1-1-222-22222-2-2-2-2-111-111-1-1-1-11111-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333-222-2000011-1-1-1-111−3−33333−3−3000000000000000000
χ39222222-1-2-2-2-2-1-1-1-222-22222-2-2-2-2-111-111-1-1-1-11111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−32-2-220000-1-11111-1-1−3−33333−3−3000000000000000000
χ40222222-1-2-2-2-2-1-1-1-222-22222-2-2-2-2-111-111-1-1-1-11111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3-222-2000011-1-1-1-11133−3−3−3−333000000000000000000
χ41222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-111-111-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii2-22-22i2i−2i−2i-1-111-1-111−i−i−i−iiiii000000000000000000
χ42222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-111-111-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-22-22−2i−2i2i2i11-1-111-1-1iiii−i−i−i−i000000000000000000
χ43222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-111-111-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i2-22-2−2i−2i2i2i-1-111-1-111iiii−i−i−i−i000000000000000000
χ44222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2222222-111-111-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-22-222i2i−2i−2i11-1-111-1-1−i−i−i−iiiii000000000000000000
χ4522-2-2-22222-2-2-2-2222-2-2-222-22-22-2-2222-2-222-2-222-2-22-22-22i2i−2i−2i2i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000
χ4622-2-2-22222-2-2-2-2222-2-2-222-22-22-2-2222-2-222-2-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000
χ4722-2-2-22222-2-2-2-222-22-22-22-2-22-22-2222-2-222-2-222-2-2-22-2200000000-22-22000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ4822-2-2-22222-2-2-2-222-22-22-22-2-22-22-2222-2-222-2-222-2-2-22-2200000000-22-2200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ4922-2-2-22222-2-2-2-22-2222-2-2-222-2-22-2-2-2222-2-22222-2-22-2-22000000002-2-220000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ5022-2-2-22222-2-2-2-22-2222-2-2-222-2-22-2-2-2222-2-22222-2-22-2-22000000002-2-22000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ5122-2-2-22222-2-2-2-22-2-2-2222-22-222-2-2-2-2222-2-22222-2-2-222-200000000-222-2000000000000000000000000000000000000000000000000002-22-20000
χ5222-2-2-22222-2-2-2-22-2-2-2222-22-222-2-2-2-2222-2-22222-2-2-222-200000000-222-200000000000000000000000000000000000000000000000000-22-220000
χ5322-2-2-222-2-222-2-22222-2-2-2-22-222-2-2222-2-2-2-222-2-2222-2-2200000000-222-2000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-2-222-2-222-2-22222-2-2-2-22-222-2-2222-2-2-2-222-2-2222-2-2200000000-222-200000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-2-222-2-222-2-222-2-2-222-222-2-22-2222-2-2-2-222-2-222-222-2000000002-2-220000000000000000000000000000000000000000000000000000002-2-22
χ5622-2-2-222-2-222-2-222-2-2-222-222-2-22-2222-2-2-2-222-2-222-222-2000000002-2-22000000000000000000000000000000000000000000000000000000-222-2
χ5722-2-2-222-2-222-2-22-22-22-222-2-22-22-2-2-222222-2-2-2-2222-22-200000000-22-22000000000000000000002-2-22000000002-22-2-22-22000000000000000000
χ5822-2-2-222-2-222-2-22-22-22-222-2-22-22-2-2-222222-2-2-2-2222-22-200000000-22-2200000000000000000000-222-200000000-22-222-22-2000000000000000000
χ5922-2-2-222-2-222-2-22-2-2222-22-22-22-2-2-2-222222-2-2-2-222-22-2222-2-2-2-2222-22-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000
χ6022-2-2-222-2-222-2-22-2-2222-22-22-22-2-2-2-222222-2-2-2-222-22-22-2-22222-2-22-22-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000
χ6122-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-111-1-111-11-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii−i−iii−i−iii00000000−i3i3−i3i3−i3i3−i3i33−3−333−3−33000000000000000000
χ6222-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-111-1-111-11-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii−i−iii−i−iii00000000i3−i3i3−i3i3−i3i3−i3−333−3−333−3000000000000000000
χ6322-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-111-1-111-11-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−iii−i−iii−i−i00000000−i3i3−i3i3−i3i3−i3i3−333−3−333−3000000000000000000
χ6422-2-2-22-122-2-211-122-2-2-222-22-22-21-1-1-111-1-111-1-111-11-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−iii−i−iii−i−i00000000i3−i3i3−i3i3−i3i3−i33−3−333−3−33000000000000000000
χ6522-2-2-22-122-2-211-12-22-22-22-2-22-221-1-1-111-1-111-1-1111-11-1000000001-11-133−3−3−3−33333−3−3−3−33300002i−2i2i−2i−i3i3−i3i3i3−i3i3−i3−ii−ii−ii−ii000000000000000000
χ6622-2-2-22-122-2-211-12-22-22-22-2-22-221-1-1-111-1-111-1-1111-11-1000000001-11-133−3−3−3−33333−3−3−3−3330000−2i2i−2i2ii3−i3i3−i3−i3i3−i3i3i−ii−ii−ii−i000000000000000000
χ6722-2-2-22-122-2-211-12-22-22-22-2-22-221-1-1-111-1-111-1-1111-11-1000000001-11-1−3−33333−3−3−3−33333−3−300002i−2i2i−2ii3−i3i3−i3−i3i3−i3i3−ii−ii−ii−ii000000000000000000
χ6822-2-2-22-122-2-211-12-22-22-22-2-22-221-1-1-111-1-111-1-1111-11-1000000001-11-1−3−33333−3−3−3−33333−3−30000−2i2i−2i2i−i3i3−i3i3i3−i3i3−i3i−ii−ii−ii−i000000000000000000
χ6922-2-2-22-1-2-22211-1-22-22-222-2-22-22111-1-1-1-1-11111-1-1-11-11000000001-11-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300002-2-22−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000000000
χ7022-2-2-22-1-2-22211-1-22-22-222-2-22-22111-1-1-1-1-11111-1-1-11-11000000001-11-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000-222-2i3−i3−i3i3−i3i3i3−i31-11-1-11-11000000000000000000
χ7122-2-2-22-1-2-22211-1-22-22-222-2-22-22111-1-1-1-1-11111-1-1-11-11000000001-11-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300002-2-22i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000000000
χ7222-2-2-22-1-2-22211-1-22-22-222-2-22-22111-1-1-1-1-11111-1-1-11-11000000001-11-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000-222-2−i3i3i3−i3i3−i3−i3i31-11-1-11-11000000000000000000
χ7322-2-2-22-1-2-22211-1-2-2222-22-22-22-2111-1-1-1-1-11111-1-11-11-122-2-2-2-222-11-11-1-111-1-11111-1-111-1-100000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ7422-2-2-22-1-2-22211-1-2-2222-22-22-22-2111-1-1-1-1-11111-1-11-11-122-2-2-2-222-11-11-1-111-1-11111-1-111-1-100000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ7522-2-2-22-1-2-22211-1-2-2222-22-22-22-2111-1-1-1-1-11111-1-11-11-1-2-22222-2-2-11-1111-1-111-1-1-1-111-1-11100000000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ7622-2-2-22-1-2-22211-1-2-2222-22-22-22-2111-1-1-1-1-11111-1-11-11-1-2-22222-2-2-11-1111-1-111-1-1-1-111-1-11100000000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ77444444-24444-2-2-2-44-4-44-4-4-444-4-4-222-2222222-2-2-2-2-2-22200000000-2-2220000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.