Finite Group Databasebeta

← Group #10797450

Character table — Group #10797450

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111112222222222222222222222222222444444444444444444444444444444444444444488888888888888888888121212121212121212121212121212122424242424242424
order12224444222222344444466666661212121212121212444444446666888888881212121212121212121212121212121212121212444412121212121212122424242424242424444444448888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ13111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ14111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111-1-1-1-1111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ171111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1ii−i−iii−i−i1111iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iii−ii−ii-11-11
χ191111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1−i−iii−i−iii1111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−i−iii11-1-111-1-1−i−iii−i−iiii−ii−i-11-11
χ201111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1−i−iii−i−iii1111iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ211111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1ii−i−iii−i−i1111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i−ii−ii-11-11
χ221111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1ii−i−iii−i−i1111−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111ii−i−iii−i−i-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ231111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ241111-1-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1−i−iii−i−iii1111−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−ii−ii−i-11-11
χ251111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1ii−i−i−i−iii-111-1ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iiii−i−ii1-1-11
χ261111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1ii−i−i−i−iii-111-1ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i−iii−i-111-1
χ271111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1ii−i−i−i−iii-111-1−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−ii−i−ii-111-1
χ281111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1ii−i−i−i−iii-111-1−i−iiiii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii−iii−i1-1-11
χ291111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1−i−iiiii−i−i-111-1ii−i−i−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii−iii−i-111-1
χ301111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1−i−iiiii−i−i-111-1ii−i−i−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−ii−i−ii1-1-11
χ311111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1−i−iiiii−i−i-111-1−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i−iii−i1-1-11
χ321111-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111-1-11111-1-1−i−iiiii−i−i-111-1−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iiii−i−ii-111-1
χ3322222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ3422222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000000000000000
χ3522222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122222222-1-1-1-11111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ3622222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-1-1-1-1-1-1-1-111111111000000000000000000000000
χ37222222222-2-2-2-22-12-2-2-2-221111-1-1-1-1-11111-1-12222-2-2-2-2-111-12222-2-2-2-2-1-111-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ38222222222-2-2-2-22-12-2-2-2-221111-1-1-1-1-11111-1-12222-2-2-2-2-111-1-2-2-2-22222-1-111-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ39222222222-2-2-2-22-12-2-2-2-221111-1-1-1-1-11111-1-1-2-2-2-22222-111-12222-2-2-2-2-1-11111111111-1-1-1-1-1-1-1-1-2-2221111-1-1-1-1-1-1-1-11111000000000000000000000000
χ40222222222-2-2-2-22-12-2-2-2-221111-1-1-1-1-11111-1-1-2-2-2-22222-111-1-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-122-2-2-1-1-1-111111111-1-1-1-1000000000000000000000000
χ4122222222-222-2-2-22-2-2-222-222222222222222200000000-2-2-2-200000000-2-2-2-2000000000000000000000000000000000000000000002-22-22-22-200000000
χ4222222222-222-2-2-22-2-2-222-222222222222222200000000-2-2-2-200000000-2-2-2-200000000000000000000000000000000000000000000-22-22-22-2200000000
χ4322222222-2-2-222-22-222-2-2-2-2-2-2-222222-2-2-2-22200000000-222-200000000-2-222000000000000000000000000000000000000000000002-22-2-22-2200000000
χ4422222222-2-2-222-22-222-2-2-2-2-2-2-222222-2-2-2-22200000000-222-200000000-2-22200000000000000000000000000000000000000000000-22-222-22-200000000
χ452222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000222200000000-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ462222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000222200000000-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ472222-2-2-2-22-2-2-2-222-22222-2-2-2-2-2222-2-22222-2-2000000002-2-2200000000-2-222000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ482222-2-2-2-22-2-2-2-222-22222-2-2-2-2-2222-2-22222-2-2000000002-2-2200000000-2-22200000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ492222-2-2-2-2-222-2-2-2-1222-2-22-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i11112i2i−2i−2i2i2i−2i−2i-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii2-22-2-1-111-1-111−i−iii−i−iii000000000000000000000000
χ502222-2-2-2-2-222-2-2-2-1222-2-22-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i1111−2i−2i2i2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-22-2211-1-111-1-1ii−i−iii−i−i000000000000000000000000
χ512222-2-2-2-2-222-2-2-2-1222-2-22-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i11112i2i−2i−2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-22-2211-1-111-1-1−i−iii−i−iii000000000000000000000000
χ522222-2-2-2-2-222-2-2-2-1222-2-22-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i1111−2i−2i2i2i−2i−2i2i2i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i2-22-2-1-111-1-111ii−i−iii−i−i000000000000000000000000
χ532222-2-2-2-2-2-2-222-2-12-2-22221111-1-1-111-1-1-1-1112i2i−2i−2i−2i−2i2i2i1-1-112i2i−2i−2i−2i−2i2i2i-1-111−i−i−i−iiiiiiiii−i−i−i−i2-2-22-1-11111-1-1−i−iiiii−i−i000000000000000000000000
χ542222-2-2-2-2-2-2-222-2-12-2-22221111-1-1-111-1-1-1-1112i2i−2i−2i−2i−2i2i2i1-1-11−2i−2i2i2i2i2i−2i−2i-1-111−i−i−i−iiiiiiiii−i−i−i−i-222-211-1-1-1-111ii−i−i−i−iii000000000000000000000000
χ552222-2-2-2-2-2-2-222-2-12-2-22221111-1-1-111-1-1-1-111−2i−2i2i2i2i2i−2i−2i1-1-112i2i−2i−2i−2i−2i2i2i-1-111iiii−i−i−i−i−i−i−i−iiiii-222-211-1-1-1-111−i−iiiii−i−i000000000000000000000000
χ562222-2-2-2-2-2-2-222-2-12-2-22221111-1-1-111-1-1-1-111−2i−2i2i2i2i2i−2i−2i1-1-11−2i−2i2i2i2i2i−2i−2i-1-111iiii−i−i−i−i−i−i−i−iiiii2-2-22-1-11111-1-1ii−i−i−i−iii000000000000000000000000
χ5722-2-222-2-222-22-2-2222-22-2-222-2-22-2-2-2-222-2-2220000000022-2-22-22-22-22-22-22-200000000000000000000000000002-22-22-22-2000000000000000000000000
χ5822-2-222-2-222-22-2-2222-22-2-222-2-22-2-2-2-222-2-2220000000022-2-2-22-22-22-222-22-20000000000000000000000000000-22-22-22-22000000000000000000000000
χ5922-2-222-2-222-22-2-2-122-22-2-2-1-111-11111-1-111-1-100000000-1-1112-22-22-22-2-11-1133−3−333−3−333−3−333−3−300003−33−33−33−3-11-11-11-11000000000000000000000000
χ6022-2-222-2-222-22-2-2-122-22-2-2-1-111-11111-1-111-1-100000000-1-1112-22-22-22-2-11-11−3−333−3−333−3−333−3−3330000−33−33−33−33-11-11-11-11000000000000000000000000
χ6122-2-222-2-222-22-2-2-122-22-2-2-1-111-11111-1-111-1-100000000-1-111-22-22-22-22-11-1133−3−333−3−333−3−333−3−30000−33−33−33−331-11-11-11-1000000000000000000000000
χ6222-2-222-2-222-22-2-2-122-22-2-2-1-111-11111-1-111-1-100000000-1-111-22-22-22-22-11-11−3−333−3−333−3−333−3−33300003−33−33−33−31-11-11-11-1000000000000000000000000
χ6322-2-222-2-22-22-22-222-22-22-2-2-2222-2-2-2-2-2-22222000000002-22-22-22-2-22-222-2-2200000000000000000000000000002-22-2-22-22000000000000000000000000
χ6422-2-222-2-22-22-22-222-22-22-2-2-2222-2-2-2-2-2-22222000000002-22-2-22-222-22-22-2-220000000000000000000000000000-22-222-22-2000000000000000000000000
χ6522-2-222-2-22-22-22-2-12-22-22-211-1-1-1111111-1-1-1-100000000-11-112-22-2-22-22-111-133−3−333−3−3−3−333−3−33300003−33−3−33−33-11-111-11-1000000000000000000000000
χ6622-2-222-2-22-22-22-2-12-22-22-211-1-1-1111111-1-1-1-100000000-11-112-22-2-22-22-111-1−3−333−3−33333−3−333−3−30000−33−333−33−3-11-111-11-1000000000000000000000000
χ6722-2-222-2-22-22-22-2-12-22-22-211-1-1-1111111-1-1-1-100000000-11-11-22-222-22-2-111-133−3−333−3−3−3−333−3−3330000−33−333−33−31-11-1-11-11000000000000000000000000
χ6822-2-222-2-22-22-22-2-12-22-22-211-1-1-1111111-1-1-1-100000000-11-11-22-222-22-2-111-1−3−333−3−33333−3−333−3−300003−33−3−33−331-11-1-11-11000000000000000000000000
χ6922-2-222-2-2-22-2-2222-2-222-2222-2-22-2-2-2-222-2-22200000000-2-22200000000-22-220000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.