Finite Group Databasebeta

← Group #72271663

Character table — Group #72271663

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111222222222222224444444444444444444444444444888888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616161616323232323232323232323232484848484848484848484848484848489696969696969696
order122222222236666666222222222222444466666666666622224466666666121212121212121244444444444444446666121212121212121212121212121212121212121212121212121212121212121288882424242424242424222244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iiiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-11-11-11-11-111-1-111-1-1ii−i−iii−i−i
χ101-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111ii−i−iii−i−iiiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1-11-11-11-11-1-111-1-111−i−iii−i−iii
χ111-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111ii−i−iii−i−i−i−i−i−iiiii11-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-111111-1-111-1-1111-1-1-1-111ii−i−i−i−iii
χ121-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111ii−i−iii−i−i−i−i−i−iiiii11-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-11111-111-1-111-1-1-11111-1-1−i−iiiii−i−i
χ131-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111−i−iii−i−iiiiiii−i−i−i−i11-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-111111-1-111-1-1111-1-1-1-111−i−iiiii−i−i
χ141-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111−i−iii−i−iiiiiii−i−i−i−i11-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111-111-1-111-1-1-11111-1-1ii−i−i−i−iii
χ151-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-11-11-11-11-111-1-111-1-1−i−iii−i−iii
χ161-1-111-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-11111-1-1-1-111-1-1-1-111−i−iii−i−iii−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1-11-11-11-11-1-111-1-111ii−i−iii−i−i
χ172222222222222222222222-2-22222-2-2-2-2-2-22222222222222-22-2-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000002-22-2
χ182222222222222222222222-2-22222-2-2-2-2-2-22222222222222-22-2-2-222-2-222-2-2-2-2-2-2-2-2-2-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000-22-22
χ1922222222222222222222-2-22222-2-222-2-2-2-2222222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000-22-220000000000000000000000000000000000000000000000000000000000002-22-20000
χ2022222222222222222222-2-22222-2-222-2-2-2-2222222222222-22-22-2-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000-22-22000000000000000000000000000000000000000000000000000000000000-22-220000
χ2122222222222222222222-2-2-2-222-2-2-2-22222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2000000000000000000000000000000002-22-222-2-222-2-2000000000000000000000000
χ2222222222222222222222-2-2-2-222-2-2-2-22222222222222222-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-200000000000000000000000000000000-22-22-2-222-2-222000000000000000000000000
χ23222222222222222222-2-22222-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222222222-2-2-2-22222-2-2-2-200000000-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000000000000
χ24222222222222222222-2-22222-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222222222222222-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000000000
χ25222222222222222222-2-222-2-2-2-222-2-2222222-2-2-2-222-2-2-2-2-22-22-2-222-2-222-2-2-2-2-2-222220000000000000000-22-2200000000000000000000000000000000000000000000002200220000-2-2-2-200000000
χ26222222222222222222-2-222-2-2-2-222-2-2222222-2-2-2-222-2-2-2-2-22-22-2-222-2-222-2-2-2-2-2-222220000000000000000-22-220000000000000000000000000000000000000000000000-2-200-2-20000222200000000
χ27222222222222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-2-2-22-22-2-2-2-2-222-2-222-2-2-2-2222200000000000000002-22-20000000000000000000000000000000000000000000022002200-2-2-2-2000000000000
χ28222222222222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-2-2-22-22-2-2-2-2-222-2-222-2-2-2-2222200000000000000002-22-200000000000000000000000000000000000000000000-2-200-2-2002222000000000000
χ29222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i222200000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ30222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i22220000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ312222222222-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000
χ322222222222-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-211111111000000000000000000000000
χ332222222222-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000000000000000
χ342222222222-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1111111111111111111111111111111112222-1-1-1-1-1-1-1-1000000000000000000000000
χ352222222222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-100000000000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32-22-2-1-111-1-111000000000000000000000000
χ362222222222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-100000000000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-22-2211-1-111-1-1000000000000000000000000
χ372222222222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-100000000000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-22-2211-1-111-1-1000000000000000000000000
χ382222222222-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-100000000000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32-22-2-1-111-1-111000000000000000000000000
χ392222222222-1-1-1-1-1-1-1-1-2-22222-2-22222-2-2-2-2-1-11111-1-11111-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-2000000001111-1-1-1-11111-1-1-1-1111133−3−3−3−33333−3−3−3−33300003−33−33−33−3000000000000000000000000
χ402222222222-1-1-1-1-1-1-1-1-2-22222-2-22222-2-2-2-2-1-11111-1-11111-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-2000000001111-1-1-1-11111-1-1-1-11111−3−33333−3−3−3−33333−3−30000−33−33−33−33000000000000000000000000
χ412222222222-1-1-1-1-1-1-1-1-2-22222-2-22222-2-2-2-2-1-11111-1-11111-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-222220000000011111111-1-1-1-11111-1-1-1-133−3−3−3−33333−3−3−3−3330000−33−33−33−33000000000000000000000000
χ422222222222-1-1-1-1-1-1-1-1-2-22222-2-22222-2-2-2-2-1-11111-1-11111-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-222220000000011111111-1-1-1-11111-1-1-1-1−3−33333−3−3−3−33333−3−300003−33−33−33−3000000000000000000000000
χ432222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-11111-1-1111122222211111111-1-1-1-11111000000002i2i−2i−2i2i2i−2i−2i-1-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i−i−i−iiiii−i−i−i−iiiii00003−3−333−3−33000000000000000000000000
χ442222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-11111-1-1111122222211111111-1-1-1-11111000000002i2i−2i−2i2i2i−2i−2i-1-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i−i−i−iiiii−i−i−i−iiiii0000−333−3−333−3000000000000000000000000
χ452222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-11111-1-1111122222211111111-1-1-1-1111100000000−2i−2i2i2i−2i−2i2i2i-1-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3iiii−i−i−i−iiiii−i−i−i−i0000−333−3−333−3000000000000000000000000
χ462222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-11111-1-1111122222211111111-1-1-1-1111100000000−2i−2i2i2i−2i−2i2i2i-1-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3iiii−i−i−i−iiiii−i−i−i−i00003−3−333−3−33000000000000000000000000
χ472-2-222-2-2-2222222-2-2-2-22222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-22-2-22-2222-2-2-2-222-2-22222-2-200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000002i−2i−2i2i
χ482-2-222-2-2-2222222-2-2-2-22222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-22-2-22-2222-2-2-2-222-2-22222-2-200000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ492-2-222-2-2-2222222-2-2-2-222-2-222-2-222-2-222-2-2222222-2-2-2-2-2-2-222-2-22-2-22222-2-2-2-22222-2-20000000000000000-222-20000000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ502-2-222-2-2-2222222-2-2-2-222-2-222-2-222-2-222-2-2222222-2-2-2-2-2-2-222-2-22-2-22222-2-2-2-22222-2-20000000000000000-222-2000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ512-2-222-2-2-2222222-2-2-2-222-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2222222-2-2-2-2220000000000000000-2-222000000000000000000000000000000002-2-2222-2-2-2-222000000000000000000000000
χ522-2-222-2-2-2222222-2-2-2-222-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2222222-2-2-2-2220000000000000000-2-22200000000000000000000000000000000-222-2-2-22222-2-2000000000000000000000000
χ532-2-222-2-2-2222222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2222-22222-2-2-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i00000000-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000000000
χ542-2-222-2-2-2222222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2222-22222-2-2-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000000000
χ552-2-222-2-2-2222222-2-2-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-2-22222-222-2-2222-2-2-2-222-2-222-2-2220000000000000000-222-200000000000000000000000000000000000000000000002-2002-20000-2-22200000000
χ562-2-222-2-2-2222222-2-2-2-2-2-222-2-222-2-222-2-22222-2-2-2-2-2-22222-222-2-2222-2-2-2-222-2-222-2-2220000000000000000-222-20000000000000000000000000000000000000000000000-2200-22000022-2-200000000
χ572-2-222-2-2-2222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-222222-2-22-22-2-22222-2-2-2-222-2-22200000000000000002-2-22000000000000000000000000000000000000000000002-2002-200-2-222000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.