Finite Group Databasebeta

← Group #72260428

Character table — Group #72260428

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130
size111122222222222222222222222244444444444444444444444444444444444444444444444448888888888888888888888888888888881616161616161616323232323232323232323232
order12224444444444448888161616161616161622244444488888888161616161616161616161616161616163232323232323232323232323232323288816161616161632323232323232323232323232323232323232323232323222448888222444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-1ii−i−i-1-1-1111iii−i−i−i
χ61111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-111−i−iii111-1-1-1−i−i−iiii
χ71111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-1−i−iii-1-1-1111−i−i−iiii
χ81111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-111ii−i−i111-1-1-1iii−i−i−i
χ9111111-1-1-1-11111111111111111111-1-11-1-11-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-11-1-1
χ10111111-1-1-1-11111111111111111111-1-11-1-11-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-111
χ11111111-1-1-1-11111111111111111111-1-11-1-11-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-11-1-11-1-1-111-111
χ12111111-1-1-1-11111111111111111111-1-11-1-11-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-111-1111-1-11-1-1
χ13111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-11111-1-1-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−i-1111-1-1i−i−i−iii
χ14111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-11111-1-1-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iii1-1-1-111−iiii−i−i
χ15111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-11111-1-1-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii-1111-1-1−iiii−i−i
χ16111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-11111-1-1-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i1-1-1-111i−i−i−iii
χ171111-1-111-1-1111111111111111111-11-1-11-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111111111111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-11-1-11-1-11-1
χ181111-1-111-1-1111111111111111111-11-1-11-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111111111111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-111-111-11
χ191111-1-111-1-1111111111111111111-11-1-11-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-1-11-11-111-11
χ201111-1-111-1-1111111111111111111-11-1-11-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111111-111-11-11-1-11-1
χ211111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-11-1-111-1-1-1-111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i1-11-11-1−ii−ii−ii
χ221111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-11-1-111-1-1-1-111111111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii-11-11-11i−ii−ii−i
χ231111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-11-1-111-1-1-1-111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii1-11-11-1i−ii−ii−i
χ241111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-11-1-111-1-1-1-111111111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−i-11-11-11−ii−ii−ii
χ251111-1-1-1-111111111111111111111-1-11-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11-1-11-1-11-1-11
χ261111-1-1-1-111111111111111111111-1-11-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-111-111-1
χ271111-1-1-1-111111111111111111111-1-11-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11-1-1111-111-1
χ281111-1-1-1-111111111111111111111-1-11-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-111-1-1-11-1-11
χ291111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-111-1-1111111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11-1-1ii−i−i11-1-1-11−i−iiii−i
χ301111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-111-1-1111111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111−i−iii-1-1111-1ii−i−i−ii
χ311111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-111-1-1111111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11-1-1−i−iii11-1-1-11ii−i−i−ii
χ321111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-111-1-1111111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111ii−i−i-1-1111-1−i−iiii−i
χ3322222222222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222-2-2-2-2-2-200000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-200000000222222222-2-2-2-2-2-2-2-200000000000000002222−2−2−2−22222−2−2−2−2-2-2-200000022−2−222−2−222−2−222−2−222−2−222−2−200000000000000000000
χ352222222222222222-2-2-2-200000000222222222-2-2-2-2-2-2-2-20000000000000000−2−2−2−22222−2−2−2−22222-2-2-2000000−2−222−2−222−2−222−2−222−2−222−2−22200000000000000000000
χ36222222222222-2-2-2-200002222−2−2−2−2222-2-2-2-2-2-20000000022−2−222−2−222−2−222−2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50002−22−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000000000
χ37222222222222-2-2-2-200002222−2−2−2−2222-2-2-2-2-2-20000000022−2−222−2−222−2−222−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50002−22−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000000000
χ38222222222222-2-2-2-20000−2−2−2−22222222-2-2-2-2-2-200000000−2−222−2−222−2−222−2−222ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000−22−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000000000
χ39222222222222-2-2-2-20000−2−2−2−22222222-2-2-2-2-2-200000000−2−222−2−222−2−222−2−222−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000−22−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000000000
χ402222222222-2-222-2-2222222222222-2-2-2222-2-2-2222222-2-2-2-2-2-22222222222220000000000000000-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ412222222222-2-222-2-2-2-2-2-200000000-2-2-2222-2-2-2-2-2-2-2-2-2220000000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2222000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ422222222222-2-222-2-2-2-2-2-200000000-2-2-2222-2-2-2-2-2-2-2-2-2220000000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2222000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ432222222222-2-2-2-22200002222−2−2−2−2-2-2-2-2-2-222200000000−2−22222−2−222−2−222−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000−22−22−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ500000000000000000000
χ442222222222-2-2-2-22200002222−2−2−2−2-2-2-2-2-2-222200000000−2−22222−2−222−2−222−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000−22−22−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ500000000000000000000
χ452222222222-2-2-2-2220000−2−2−2−22222-2-2-2-2-2-22220000000022−2−2−2−222−2−222−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ70002−22−22−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ700000000000000000000
χ462222222222-2-2-2-2220000−2−2−2−22222-2-2-2-2-2-22220000000022−2−2−2−222−2−222−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ70002−22−22−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000000000000000
χ47222222-2-2-2-22222222222-2-2-2-2-2-2-2-22-2-22-2-22-2-222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000002-2-2-2-2222200000000000000000000000000000000000000000000
χ48222222-2-2-2-2222222-2-2-2-2000000002-2-22-2-22-2-2-2-22222-2-200000000000000002222−2−2−2−22222−2−2−2−2-22200000022−2−2−2−222−2−22222−2−2−2−222−2−22200000000000000000000
χ49222222-2-2-2-2222222-2-2-2-2000000002-2-22-2-22-2-2-2-22222-2-20000000000000000−2−2−2−22222−2−2−2−22222-222000000−2−22222−2−222−2−2−2−22222−2−222−2−200000000000000000000
χ50222222-2-2-2-222-2-2-2-200002222−2−2−2−22-2-2-222-2220000000022−2−222−2−2−2−222−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50002−2−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.