Finite Group Databasebeta

← Group #72227125

Character table — Group #72227125

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140
size1111222222222222222244444444444444444444444444444444444448888888888888888888888888888888888888888816161616161616163232323232323232323232323232323232323232323232323232323264646464128128
order12222244444488888888444888888888888881616161616161616161616161616161616161616888161616161616323232323232323232323232323232323232323232323232323232323232323222224444448888881616161616161616161616163232323232323232444424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ7111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1
χ91111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-1ii−i−i1-1i−i11-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1ii−i−i1-1
χ101111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-1−i−iii1-1−ii11-1-1iiii−i−i−i−i−i−iii-1-1-1-11111−i−iii-11
χ111111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111ii−i−i-11i−i-1-111−i−i−i−iiiiiii−i−i1111-1-1-1-1−i−iii-11
χ121111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111−i−iii-11−ii-1-111−i−i−i−iiiii−i−iii-1-1-1-11111ii−i−i1-1
χ131111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-1ii−i−i1-1i−i11-1-1−i−i−i−iiiiiii−i−i-1-1-1-11111ii−i−i-11
χ141111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-1−i−iii1-1−ii11-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−iii1-1
χ151111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111ii−i−i-11i−i-1-111iiii−i−i−i−iii−i−i-1-1-1-11111−i−iii1-1
χ161111-1-1-1111-1111111111-1-1111-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111−i−iii-11−ii-1-111iiii−i−i−i−i−i−iii1111-1-1-1-1ii−i−i-11
χ172222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-2-200000000000000000000000000000000000022220022000000000000-2-2-2-200000000000000
χ182222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2-2-2000000000000000000000000000000000000-2-2-2-200-2-2000000000000222200000000000000
χ192222222222222222-2-2-2-222222-222-2-2-2-2-2-222-200000000000000000000-2-2-200000022222222−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−20000222200-2-2000000000000000022−2−222−2−2000000
χ202222222222222222-2-2-2-222222-222-2-2-2-2-2-222-200000000000000000000-2-2-200000022222222−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−20000-2-2-2-200220000000000000000−2−222−2−222000000
χ212222222222222222-2-2-2-222222-222-2-2-2-2-2-222-200000000000000000000-2-2-2000000−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−2222222220000222200-2-20000000000000000−2−222−2−222000000
χ222222222222222222-2-2-2-222222-222-2-2-2-2-2-222-200000000000000000000-2-2-2000000−2−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−2222222220000-2-2-2-20022000000000000000022−2−222−2−2000000
χ23222222222222-2-2-2-22222222-2-22-2-2-2-2-2-222-2-222222222222-2-2-2-2-2-2-2-2222-2-222-2-2-2-200000000000000000000000000000000222200002200-2-2-2-200000000000000000000000000
χ24222222222222-2-2-2-22222222-2-22-2-2-2-2-2-222-2-222222222222-2-2-2-2-2-2-2-2222-2-222-2-2-2-200000000000000000000000000000000-2-2-2-20000-2-200222200000000000000000000000000
χ25222222222222-2-2-2-22222222-2-22-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-2-2-222222222-2-22-2-2-2-22222000000000000000000000000000000000000000000000000000000000000000000002-22-200
χ26222222222222-2-2-2-22222222-2-22-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-2-2-222222222-2-22-2-2-2-2222200000000000000000000000000000000000000000000000000000000000000000000-22-2200
χ272222222-2222-200002222-2-2-2002000000-2-2002222222-2-2-2-20000000022-200-2-200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−222220000-2-200000022−2−222−2−2000000000000000000
χ282222222-2222-200002222-2-2-2002000000-2-2002222222-2-2-2-20000000022-200-2-200002222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2-2-2-2-2000022000000−2−222−2−222000000000000000000
χ292222222-2222-200002222-2-2-2002000000-2-2002222222-2-2-2-20000000022-200-2-20000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2222222220000-2-2000000−2−222−2−222000000000000000000
χ302222222-2222-200002222-2-2-2002000000-2-2002222222-2-2-2-20000000022-200-2-20000−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222-2-2-2-200002200000022−2−222−2−2000000000000000000
χ31222222-22-2-2-22-2-2-2-20000-22-2220-2-20000002202−222−2−222−2−22222−2−2−2−22−20002−222−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500002-22-200000000000000002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000
χ32222222-22-2-2-22-2-2-2-20000-22-2220-2-20000002202−222−2−222−2−22222−2−2−2−22−20002−222−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ50000-22-220000000000000000−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000
χ33222222-22-2-2-22-2-2-2-20000-22-2220-2-20000002202−222−2−222−2−22222−2−2−2−22−20002−222−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500002-22-200000000000000002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000
χ34222222-22-2-2-22-2-2-2-20000-22-2220-2-20000002202−222−2−222−2−22222−2−2−2−22−20002−222−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ50000-22-220000000000000000−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000
χ35222222-22-2-2-22-2-2-2-20000-22-2220-2-2000000220−22−2−222−2−222−2−2−2−22222−22000−22−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700002-22-20000000000000000−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000
χ36222222-22-2-2-22-2-2-2-20000-22-2220-2-2000000220−22−2−222−2−222−2−2−2−22222−22000−22−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ70000-22-2200000000000000002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000
χ37222222-22-2-2-22-2-2-2-20000-22-2220-2-2000000220−22−2−222−2−222−2−2−2−22222−22000−22−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700002-22-20000000000000000−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000
χ38222222-22-2-2-22-2-2-2-20000-22-2220-2-2000000220−22−2−222−2−222−2−2−2−22222−22000−22−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ70000-22-2200000000000000002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000
χ392222-2-222-2-222-2-2-2-200002-2-222022000000-2-202−2−2−222−2−222−2−2−2−222222−20002−222−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700002i−2i−2i2i0000000000000000i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000
χ402222-2-222-2-222-2-2-2-200002-2-222022000000-2-202−2−2−222−2−222−2−2−2−222222−20002−222−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70000−2i2i2i−2i0000000000000000−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000
χ412222-2-222-2-222-2-2-2-200002-2-222022000000-2-202−2−2−222−2−222−2−2−2−222222−20002−222−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700002i−2i−2i2i0000000000000000i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000
χ422222-2-222-2-222-2-2-2-200002-2-222022000000-2-202−2−2−222−2−222−2−2−2−222222−20002−222−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70000−2i2i2i−2i0000000000000000−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000
χ432222-2-222-2-222-2-2-2-200002-2-222022000000-2-20−2222−2−222−2−22222−2−2−2−2−22000−22−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500002i−2i−2i2i0000000000000000−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.