Finite Group Databasebeta

← Group #110971

Character table — Group #110971

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222222244444444444444444444444444888888888888888888888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ10111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-111−i−iii
χ11111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−i-1-111−i−iii
χ12111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iii11-1-1ii−i−i
χ13111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii11-1-1−i−iii
χ14111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-111ii−i−i
χ15111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ16111111111-1-1-1-1-1-11-1-111-1-1111-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11-11-1i−ii−ii−ii−i1-11-1
χ18111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-11-11−ii−ii−ii−ii-11-11
χ19111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-111111-11-1i−ii−i−ii−ii-11-11
χ20111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-11-11−ii−iii−ii−i1-11-1
χ21111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-111111-11-1−ii−iii−ii−i-11-11
χ22111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-11-11i−ii−i−ii−ii1-11-1
χ23111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11-11-1−ii−ii−ii−ii1-11-1
χ24111111-1-1-1111-1-1-1-11-1-1-11111-11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-11-11i−ii−ii−ii−i-11-11
χ25111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11i−i−ii−iii−i
χ26111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1−iii−ii−i−ii
χ27111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11−iii−ii−i−ii
χ28111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1i−i−ii−iii−i
χ29111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1i−i−iii−i−ii
χ30111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11−iii−i−iii−i
χ31111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1−iii−i−iii−i
χ32111111-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11i−i−iii−i−ii
χ33222222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ35222222222-2-2-2-2-2-22-2-2-2-222-2-2-22222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ36222222222-2-2-2-2-2-22-2-2-2-222-2-2-2222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ37222222-2-2-2222-2-2-2-22-222-2-2-2-22-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ38222222-2-2-2222-2-2-2-22-222-2-2-2-22-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ39222222-2-2-2-2-2-2222-2-222222-2-222-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ40222222-2-2-2-2-2-2222-2-222222-2-222-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ412222-2-222-222-22-2-2-2-2222-2-22-2-222-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ422222-2-222-222-22-2-2-2-2222-2-22-2-222-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ432222-2-222-222-22-2-2-2-22-2-222-222-2-2200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ442222-2-222-222-22-2-2-2-22-2-222-222-2-220000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ452222-2-222-2-2-22-222-22-222222-2-2-2-220000000000000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ462222-2-222-2-2-22-222-22-222222-2-2-2-2200000000000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ472222-2-222-2-2-22-222-22-2-2-2-2-2-22222-200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ482222-2-222-2-2-22-222-22-2-2-2-2-2-22222-20000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ492222-2-2-2-2222-2-2222-2-22222-22-2-22-2000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ502222-2-2-2-2222-2-2222-2-22222-22-2-22-20000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ512222-2-2-2-2222-2-2222-2-2-2-2-2-22-222-22000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ522222-2-2-2-2222-2-2222-2-2-2-2-2-22-222-2200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ532222-2-2-2-22-2-222-2-222222-2-2-22-22-22000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ542222-2-2-2-22-2-222-2-222222-2-2-22-22-220000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ552222-2-2-2-22-2-222-2-2222-2-2222-22-22-20000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ562222-2-2-2-22-2-222-2-2222-2-2222-22-22-200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ572-22-22-22-222-22-22-2-2-220000000000002-2002-2002-2002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ582-22-22-22-222-22-22-2-2-220000000000002-2002-2002-2002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ592-22-22-22-222-22-22-2-2-22000000000000-2200-2200-2200-22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ602-22-22-22-222-22-22-2-2-22000000000000-2200-2200-2200-22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ612-22-22-22-22-22-22-22-22-20000000000002i−2i002i−2i00−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−20000000000000000
χ622-22-22-22-22-22-22-22-22-20000000000002i−2i002i−2i00−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−220000000000000000
χ632-22-22-22-22-22-22-22-22-2000000000000−2i2i00−2i2i002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−220000000000000000
χ642-22-22-22-22-22-22-22-22-2000000000000−2i2i00−2i2i002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−20000000000000000
χ652-22-22-2-22-22-222-222-2-20000000000002i−2i00−2i2i002i−2i00−2i2i2−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ662-22-22-2-22-22-222-222-2-20000000000002i−2i00−2i2i002i−2i00−2i2i−22−222−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ672-22-22-2-22-22-222-222-2-2000000000000−2i2i002i−2i00−2i2i002i−2i2−22−2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ682-22-22-2-22-22-222-222-2-2000000000000−2i2i002i−2i00−2i2i002i−2i−22−222−22−2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ692-22-22-2-22-2-22-2-22-22220000000000002-200-2200-22002-22−22−2−22−22−22−222−22−2−22−222−22−22−22−2−22−220000000000000000
χ702-22-22-2-22-2-22-2-22-22220000000000002-200-2200-22002-2−22−222−22−22−22−2−22−222−22−2−22−22−22−222−22−20000000000000000
χ712-22-22-2-22-2-22-2-22-2222000000000000-22002-2002-200-222−22−2−22−22−22−222−22−22−22−2−22−22−22−222−22−20000000000000000
χ722-22-22-2-22-2-22-2-22-2222000000000000-22002-2002-200-22−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−220000000000000000
χ732-22-2-222-2-22-2-2-2-2222200000000002-2002-2002-2002-2002−2−222−2−222−2−222−2−222−2−222−2−222−2−222−2−220000000000000000
χ742-22-2-222-2-22-2-2-2-2222200000000002-2002-2002-2002-200−222−2−222−2−222−2−222−2−222−2−222−2−222−2−222−20000000000000000
χ752-22-2-222-2-22-2-2-2-222220000000000-2200-2200-2200-22002−2−222−2−222−2−222−2−22−222−2−222−2−222−2−222−20000000000000000
χ762-22-2-222-2-22-2-2-2-222220000000000-2200-2200-2200-2200−222−2−222−2−222−2−222−22−2−222−2−222−2−222−2−220000000000000000
χ772-22-2-222-2-2-22222-22-2-200000000002i−2i002i−2i00−2i2i00−2i2i002−2−222−2−22−222−2−222−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ782-22-2-222-2-2-22222-22-2-200000000002i−2i002i−2i00−2i2i00−2i2i00−222−2−222−22−2−222−2−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ792-22-2-222-2-2-22222-22-2-20000000000−2i2i00−2i2i002i−2i002i−2i002−2−222−2−22−222−2−222−2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ802-22-2-222-2-2-22222-22-2-20000000000−2i2i00−2i2i002i−2i002i−2i00−222−2−222−22−2−222−2−22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ812-22-2-22-2222-2-222-2-22-200000000002i−2i00−2i2i002i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i22−2−22−222−22−2−22−222−20000000000000000
χ822-22-2-22-2222-2-222-2-22-200000000002i−2i00−2i2i002i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−222−22−2−22−222−22−2−220000000000000000
χ832-22-2-22-2222-2-222-2-22-20000000000−2i2i002i−2i00−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−222−22−2−22−222−22−2−220000000000000000
χ842-22-2-22-2222-2-222-2-22-20000000000−2i2i002i−2i00−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i22−2−22−222−22−2−22−222−20000000000000000
χ852-22-2-22-222-222-2-22-2-2200000000002-200-2200-22002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ862-22-2-22-222-222-2-22-2-2200000000002-200-2200-22002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ872-22-2-22-222-222-2-22-2-220000000000-22002-2002-200-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ882-22-2-22-222-222-2-22-2-220000000000-22002-2002-200-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ8988-8-800000000000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-80000000000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88000000000000008-8000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800000000000000-88000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).