Finite Group Databasebeta

← Group #495213

Character table — Group #495213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122222222222444444448888888816161616161616161616161616161616444444448888888888881616161616161616161616161616161616161616161616162222444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111-1-1-11-111-1-11-111-1-11-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ18111-1-1-11-111-1-11-111-1-11-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ19111-1-1-11-111-1-11-111-1-11-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ20111-1-1-11-111-1-11-111-1-11-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ21111-1-1-11-111-1-11-111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i11-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-11i−ii−i−ii−ii
χ22111-1-1-11-111-1-11-111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i11-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-111-1-111-1−ii−iii−ii−i
χ23111-1-1-11-111-1-11-111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii11-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-11−ii−iii−ii−i
χ24111-1-1-11-111-1-11-111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii11-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-111-1-111-1i−ii−i−ii−ii
χ25111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-11-1-11-11i−i−iii−i−ii
χ26111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-111-11-1−iii−i−iii−i
χ27111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-11-11−iii−i−iii−i
χ28111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-111-11-1i−i−iii−i−ii
χ29111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-111ii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1i−i−ii−iii−i
χ30111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii-1-111ii−i−i−i−iii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11−iii−ii−i−ii
χ31111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-111−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−iii−ii−i−ii
χ32111-1-1-11-1-1-1111-1-1-1111-111-1-111-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i-1-111−i−iiiii−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-11-1-11i−i−ii−iii−i
χ3322222222222222222222-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−22-22-22-22-200000000000022−2−222−2−222−2−222−2−222−2−222−2−20000000000000000
χ36222222222222-2-2-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−2-22-22-22-2200000000000022−2−222−2−2−2−222−2−222−2−222−2−2220000000000000000
χ37222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−222222-22-22-22-2000000000000−2−222−2−222−2−222−2−222−2−222−2−2220000000000000000
χ38222222222222-2-2-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−22222-22-22-22-22000000000000−2−222−2−22222−2−222−2−222−2−222−2−20000000000000000
χ3922222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222222222222-2-2-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−22-22-2-22-22000000000000−2−222−2−22222−2−222−2−2−2−222−2−2220000000000000000
χ4222222222-2-2-2-2-2-22222-2-2000000002222−2−2−2−22222−2−2−2−2-22-222-22-2000000000000−2−222−2−222−2−222−2−22222−2−222−2−20000000000000000
χ4322222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−222222-22-2-22-2200000000000022−2−222−2−2−2−222−2−22222−2−222−2−20000000000000000
χ4422222222-2-2-2-2-2-22222-2-200000000−2−2−2−22222−2−2−2−22222-22-222-22-200000000000022−2−222−2−222−2−222−2−2−2−222−2−2220000000000000000
χ45222-2-2-22-222-2-22-222-2-22-2-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ46222-2-2-22-222-2-22-222-2-22-2-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ47222-2-2-22-222-2-2-22-2-222-22000000002222−2−2−2−2−2−2−2−222222i−2i−2i2i2i−2i−2i2i00000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ48222-2-2-22-222-2-2-22-2-222-22000000002222−2−2−2−2−2−2−2−22222−2i2i2i−2i−2i2i2i−2i00000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ49222-2-2-22-222-2-2-22-2-222-2200000000−2−2−2−222222222−2−2−2−22i−2i−2i2i2i−2i−2i2i000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ50222-2-2-22-222-2-2-22-2-222-2200000000−2−2−2−222222222−2−2−2−2−2i2i2i−2i−2i2i2i−2i000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ51222-2-2-22-2-2-2222-2-2-2222-2-2-222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ52222-2-2-22-2-2-2222-2-2-2222-2-2-222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ53222-2-2-22-2-2-222-2222-2-2-22000000002222−2−2−2−2−2−2−2−222222i−2i−2i2i−2i2i2i−2i000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ54222-2-2-22-2-2-222-2222-2-2-22000000002222−2−2−2−2−2−2−2−22222−2i2i2i−2i2i−2i−2i2i000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ55222-2-2-22-2-2-222-2222-2-2-2200000000−2−2−2−222222222−2−2−2−22i−2i−2i2i−2i2i2i−2i00000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ56222-2-2-22-2-2-222-2222-2-2-2200000000−2−2−2−222222222−2−2−2−2−2i2i2i−2i2i−2i−2i2i00000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ572-2-22-2-2222-22-22-22-22-2-220000000022−2−222−2−222−2−222−2−20000000000002-22-22-22-22−22−22−22−22−22−22−22−22−22−22−22−20000000000000000
χ582-2-22-2-2222-22-22-22-22-2-220000000022−2−222−2−222−2−222−2−2000000000000-22-22-22-222−22−22−22−2−22−22−22−22−22−22−22−220000000000000000
χ592-2-22-2-2222-22-22-22-22-2-2200000000−2−222−2−222−2−222−2−2220000000000002-22-22-22-2−22−22−22−22−22−22−22−22−22−22−22−220000000000000000
χ602-2-22-2-2222-22-22-22-22-2-2200000000−2−222−2−222−2−222−2−222000000000000-22-22-22-22−22−22−22−222−22−22−22−22−22−22−22−20000000000000000
χ612-2-22-2-2222-22-2-22-22-222-222-2-2-2-2220000000000000000000000002-22-200000000000000002-2-222-2-222-2-222-2-220000000000000000
χ622-2-22-2-2222-22-2-22-22-222-222-2-2-2-2220000000000000000000000002-22-20000000000000000-222-2-222-2-222-2-222-20000000000000000
χ632-2-22-2-2222-22-2-22-22-222-2-2-22222-2-222-2-2-2-22222-2-2-2-22200000000-22-22000000002-2-222-2-2200000000000000000000000000000000
χ642-2-22-2-2222-22-2-22-22-222-2-2-22222-2-2-2-22222-2-2-2-22222-2-200000000-22-2200000000-222-2-222-200000000000000000000000000000000
χ652-2-22-2-222-22-222-2-22-22-220000000022−2−222−2−222−2−222−2−20000000000002-22-2-22-22−22−22−22−222−22−22−22−2−22−22−22−220000000000000000
χ662-2-22-2-222-22-222-2-22-22-220000000022−2−222−2−222−2−222−2−2000000000000-22-222-22-2−22−22−22−22−22−22−22−222−22−22−22−20000000000000000
χ672-2-22-2-222-22-222-2-22-22-2200000000−2−222−2−222−2−222−2−2220000000000002-22-2-22-222−22−22−22−2−22−22−22−222−22−22−22−20000000000000000
χ682-2-22-2-222-22-222-2-22-22-2200000000−2−222−2−222−2−222−2−222000000000000-22-222-22-22−22−22−22−22−22−22−22−2−22−22−22−220000000000000000
χ692-2-22-2-222-22-22-222-22-22-222-2-2-2-222000000000000000000000000-22-2200000000000000002-2-222-2-22-222-2-222-20000000000000000
χ702-2-22-2-222-22-22-222-22-22-222-2-2-2-222000000000000000000000000-22-220000000000000000-222-2-222-22-2-222-2-220000000000000000
χ712-2-22-2-222-22-22-222-22-22-2-2-22222-2-222-2-2-2-22222-2-2-2-222000000002-22-200000000-222-2-222-200000000000000000000000000000000
χ722-2-22-2-222-22-22-222-22-22-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000002-22-2000000002-2-222-2-2200000000000000000000000000000000
χ732-2-2-2222-22-2-22222-2-22-2-20000000022−2−222−2−2−2−222−2−2220000000000002i−2i−2i2i2i−2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ742-2-2-2222-22-2-22222-2-22-2-20000000022−2−222−2−2−2−222−2−222000000000000−2i2i2i−2i−2i2i2i−2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ752-2-2-2222-22-2-22222-2-22-2-200000000−2−222−2−22222−2−222−2−20000000000002i−2i−2i2i2i−2i−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ762-2-2-2222-22-2-22222-2-22-2-200000000−2−222−2−22222−2−222−2−2000000000000−2i2i2i−2i−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ772-2-2-2222-22-2-22-2-2-222-2222222-2-2-2-20000000000000000000000002-2-2200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000
χ782-2-2-2222-22-2-22-2-2-222-2222222-2-2-2-20000000000000000000000002-2-220000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000
χ792-2-2-2222-22-2-22-2-2-222-222-2-2-2-2222222-2-2-2-222-2-22222-2-200000000-222-2000000002-2-22-222-200000000000000000000000000000000
χ802-2-2-2222-22-2-22-2-2-222-222-2-2-2-22222-2-22222-2-222-2-2-2-22200000000-222-200000000-222-22-2-2200000000000000000000000000000000
χ812-2-2-2222-2-222-222-222-2-2-20000000022−2−222−2−2−2−222−2−2220000000000002i−2i−2i2i−2i2i2i−2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.