Finite Group Databasebeta

← Group #72225534

Character table — Group #72225534

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142
size1122222224444444444444444444444444444448888888888888888888888816161616161616161616161616161616161616161616161616161616161616161616161616161616161616166464646464646464646464646464646464646464646464646464646464646464256256256256
order1224488882444448888888888881616161616161616161616168888816161616161616161616323232323232323216161616161616161616161616161616323232323232323232323232323232323232323232323232323232324488161616163232323232323232646464646464646464646464646464642488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ9111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1i−i
χ10111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−iii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-11−ii
χ11111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-11−ii
χ12111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii−ii−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-111111-1i−i
χ13111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-111111-1−ii
χ14111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiii−ii−iii−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-11i−i
χ15111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-11i−i
χ16111111111-111-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−ii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii
χ17222222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ19222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000002222222200000000-2-2-2-2-2-2-2-2000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000002222222200000000-2-2-2-2-2-2-2-20000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000-2-2-2-2-2-2-2-20000000022222222000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000-2-2-2-2-2-2-2-200000000222222220000000000000000−2−222−2−22222−2−222−2−20000
χ23222222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22-2-2-2-222-2-22222-2-2222222220000000000000000222200000000-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000
χ24222222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22-2-2-2-222-2-22222-2-2222222220000000000000000222200000000-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ25222222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22-2-2-2-222-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2000000002222222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ26222222222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22-2-2-2-222-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-200000000222222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ27222222222-222-2-2-22222222222-2-2222222-2-2-2-222-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ28222222222-222-2-2-22222222222-2-2222222-2-2-2-222-2-2-2-2-2-2-222-2-222-2-2-2-2-2-22222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ29222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-22222222222-2-2-2-200000000000000000000000000002i2i2i2i−2i−2i−2i−2i00000000−2i−2i−2i−2i2i2i2i2i0000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000
χ30222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-22222222222-2-2-2-200000000000000000000000000002i2i2i2i−2i−2i−2i−2i00000000−2i−2i−2i−2i2i2i2i2i0000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000
χ31222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-22222222222-2-2-2-20000000000000000000000000000−2i−2i−2i−2i2i2i2i2i000000002i2i2i2i−2i−2i−2i−2i0000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000
χ32222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222-22222222222-2-2-2-20000000000000000000000000000−2i−2i−2i−2i2i2i2i2i000000002i2i2i2i−2i−2i−2i−2i0000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000
χ33222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-200000000-2-2-2-22222000000002i−2i2i−2i−2i−2i2i2i0000000000000000000000000000
χ34222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-200000000-2-2-2-2222200000000−2i2i−2i2i2i2i−2i−2i0000000000000000000000000000
χ35222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-22222-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-222000000002222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ36222222222-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-22222-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-222000000002222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-20000002200002222−2−222−2−2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22−22−22i2i−2i−2i2i2i−2i−2i22−2−222−2−2000000000000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ382222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-20000002200002222−2−222−2−2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22−22−22i2i−2i−2i2i2i−2i−2i22−2−222−2−2000000000000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ392222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-20000002200002222−2−222−2−2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22−22−2−2i−2i2i2i−2i−2i2i2i22−2−222−2−2000000000000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ402222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-20000002200002222−2−222−2−2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22−22−2−2i−2i2i2i−2i−2i2i2i22−2−222−2−2000000000000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ412222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−222i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−22−22−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000000000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ422222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−222i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−22−22−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000000000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ432222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−222−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−22−222i2i−2i−2i2i2i−2i−2i−2−222−2−222000000000000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ442222222-2-22-2-22-2-2000000002-222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−222−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−22−222i2i−2i−2i2i2i−2i−2i−2−222−2−222000000000000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ452222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-222−2−2−2−2222222−2−2−2−2−2−2−2−222222−2−2222-2-2-2-22222−2−2−2−222000000000000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ462222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-222−2−2−2−2222222−2−2−2−2−2−2−2−222222−2−2222-2-2-2-22222−2−2−2−222000000000000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ472222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-222−2−2−2−222−2−2−2−222222222−2−2−2−22−2−22-2-22222-2-222−2−2−2−222000000000000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ482222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-222−2−2−2−222−2−2−2−222222222−2−2−2−22−2−22-2-22222-2-222−2−2−2−222000000000000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ492222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-2−2−22222−2−22222−2−2−2−2−2−2−2−22222−222−2-2-22222-2-2−2−22222−2−2000000000000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ502222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-2−2−22222−2−22222−2−2−2−2−2−2−2−22222−222−2-2-22222-2-2−2−22222−2−2000000000000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ512222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-2−2−22222−2−2−2−2−2−222222222−2−2−2−2−222−222-2-2-2-222−2−22222−2−2000000000000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ522222222-2-2-2-2-2-222000000002-2-2-2-2-200002222-2-22000000220000-2-2−2−22222−2−2−2−2−2−222222222−2−2−2−2−222−222-2-2-2-222−2−22222−2−2000000000000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.