Finite Group Databasebeta

← Group #72225490

Character table — Group #72225490

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134
size112222222222222224444444444444444444444444444444444444444448888888888888888888888888888888888888883232323232323232323232323232323232323232323232323232323232323232128128128128
order1224488881616161616161616244444888888888888161616161616161616161616161616163232323232323232888881616161616163232323232323232323232323232323232323232323232323232323232323232323232323232323232323232646464646464646464646464646464648888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−i
χ611111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−iii
χ711111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−iii
χ811111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111ii−i−i
χ9111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ10111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ12111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ13111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i
χ14111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii
χ15111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii
χ16111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i
χ17222222222222222222222222222222222222222222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222-2-222-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222222222222000000000000000000000000000000000000
χ192222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22222000000002-2-2-2-2-2-2-2-2220000000000000000000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ202222222222222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-22222000000002-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ212222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-200000000-222222222-2-20000000000000000000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-200000000-222222222-2-200000000000000000000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ23222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ24222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222222222222222-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2000000000000000000000000000000000000
χ25222222222-2-2-2-2-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222-2-2-2-2-2-200000000000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ26222222222-2-2-2-2-2-2-2-2222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222-2-2-2-2-2-200000000000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ27222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2-222222200000000000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000
χ28222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2-222222200000000000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000
χ292222222-2-20000222222-2-2-2-2-2-2000000002-200000022-2-2-2-20000222222222000022-2-200222200000000-2-2-2-200000000-2-2-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ302222222-2-20000222222-2-2-2-2-2-2000000002-200000022-2-2-2-20000222222222000022-2-200222200000000-2-2-2-200000000-2-2-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ312222222-2-20000222222-2-2-2-2-2-2000000002-200000022-2-2-2-20000-2-2-2-2-2-2-2-22000022-2-200-2-2-2-200000000222200000000222222−2−2−2−22222−2−2−2−22200000000000000000000
χ322222222-2-20000222222-2-2-2-2-2-2000000002-200000022-2-2-2-20000-2-2-2-2-2-2-2-22000022-2-200-2-2-2-2000000002222000000002222−2−22222−2−2−2−22222−2−200000000000000000000
χ332222222-2-200002222-2-2-2-22222000000002-200000022-2-2-2-2000022222222-20000-2-22200-2-2-2-200000000-2-2-2-200000000222222−2−222−2−2−2−222−2−22200000000000000000000
χ342222222-2-200002222-2-2-2-22222000000002-200000022-2-2-2-2000022222222-20000-2-22200-2-2-2-200000000-2-2-2-2000000002222−2−222−2−22222−2−222−2−200000000000000000000
χ352222222-2-200002222-2-2-2-22222000000002-200000022-2-2-2-20000-2-2-2-2-2-2-2-2-20000-2-22200222200000000222200000000-2-2-2-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ362222222-2-200002222-2-2-2-22222000000002-200000022-2-2-2-20000-2-2-2-2-2-2-2-2-20000-2-22200222200000000222200000000-2-2-2-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ3722222-2-2222222000022-2-2-2-22200000000-2222-2-2-2-200000022222222−2−2−2−2-200000000-2-222−2−22222−2−2−2−222−2−22222−2−2−2−222−2−20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ3822222-2-2222222000022-2-2-2-22200000000-2222-2-2-2-200000022222222−2−2−2−2-200000000-2-222−2−22222−2−2−2−222−2−22222−2−2−2−222−2−20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ3922222-2-2222222000022-2-2-2-22200000000-2222-2-2-2-20000002222−2−2−2−22222-200000000-2-2−2−222−2−2−2−22222−2−222−2−2−2−22222−2−2220000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ4022222-2-2222222000022-2-2-2-22200000000-2222-2-2-2-20000002222−2−2−2−22222-200000000-2-2−2−222−2−2−2−22222−2−222−2−2−2−22222−2−2220000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ4122222-2-22222220000-2-2-2-222-2-200000000-2222-2-2-2-2000000-2-2-2-22222−2−2−2−220000000022−2−2222222−2−2−2−222−2−2−2−2−2−22222−2−2220000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ4222222-2-22222220000-2-2-2-222-2-200000000-2222-2-2-2-2000000-2-2-2-22222−2−2−2−220000000022−2−2222222−2−2−2−222−2−2−2−2−2−22222−2−2220000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ4322222-2-22222220000-2-2-2-222-2-200000000-2222-2-2-2-2000000-2-2-2-2−2−2−2−222222000000002222−2−2−2−2−2−22222−2−2222222−2−2−2−222−2−20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ4422222-2-22222220000-2-2-2-222-2-200000000-2222-2-2-2-2000000-2-2-2-2−2−2−2−222222000000002222−2−2−2−2−2−22222−2−2222222−2−2−2−222−2−20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ4522222-2-222-2-2-2-2000022-2-2-2-22200000000-22-2-22222000000-2-2-2-22222−2−2−2−2-2000000002222−2−2−2−2−2−2222222−2−2−2−2−2−2222222−2−20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ4622222-2-222-2-2-2-2000022-2-2-2-22200000000-22-2-22222000000-2-2-2-22222−2−2−2−2-2000000002222−2−2−2−2−2−2222222−2−2−2−2−2−2222222−2−20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ4722222-2-222-2-2-2-2000022-2-2-2-22200000000-22-2-22222000000-2-2-2-2−2−2−2−22222-20000000022−2−2222222−2−2−2−2−2−2222222−2−2−2−2−2−2220000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ4822222-2-222-2-2-2-2000022-2-2-2-22200000000-22-2-22222000000-2-2-2-2−2−2−2−22222-20000000022−2−2222222−2−2−2−2−2−2222222−2−2−2−2−2−2220000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ4922222-2-222-2-2-2-20000-2-2-2-222-2-200000000-22-2-2222200000022222222−2−2−2−2200000000-2-2−2−222−2−2−2−2222222−2−22222−2−2−2−2−2−2220000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ5022222-2-222-2-2-2-20000-2-2-2-222-2-200000000-22-2-2222200000022222222−2−2−2−2200000000-2-2−2−222−2−2−2−2222222−2−22222−2−2−2−2−2−2220000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ5122222-2-222-2-2-2-20000-2-2-2-222-2-200000000-22-2-222220000002222−2−2−2−22222200000000-2-222−2−22222−2−2−2−2−2−222−2−2−2−2222222−2−20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ5222222-2-222-2-2-2-20000-2-2-2-222-2-200000000-22-2-222220000002222−2−2−2−22222200000000-2-222−2−22222−2−2−2−2−2−222−2−2−2−2222222−2−20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ5322-22-2220022−2−2222200002i−2i2i−2i2222−2−2−2−2-202−222−2−2-2-20000i2i2−i2−i222-2-222-2-20i2i2−i2−i2002i−2ii2−i2000022−2−222−2−20000i2i2−i2−i2i2i2−i2−i22i−2i2i−2iζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ700000000000000000000
χ5422-22-2220022−2−2222200002i−2i2i−2i2222−2−2−2−2-202−222−2−2-2-20000i2i2−i2−i222-2-222-2-20i2i2−i2−i2002i−2ii2−i2000022−2−222−2−20000i2i2−i2−i2i2i2−i2−i22i−2i2i−2i−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ700000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.