Finite Group Databasebeta

← Group #109039

Character table — Group #109039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222222444444444444448888888888888888444488888888888888888888888888888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1111111-1-11111-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1111111-1-11111-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ181111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ191111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ201111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ211111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ221111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ231111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ241111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1-111-1
χ261111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-111-1-11
χ271111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-111-1-11
χ281111-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1-111-1
χ291111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ301111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ311111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ321111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ3322222222222222-2-222-2-222-2-2-2-2220000000000000000-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ3422222222222222-2-222-2-222-2-2-2-2220000000000000000-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-20000000000000000222222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-200000000000000002222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ3722222222-2-222-2-222-2-222-2-2-2-2-2-22200000000000000002-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-222-2-222-2-222-2-2-2-2-2-22200000000000000002-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-22222-2-2-2-2-22-22000000000000000022-2-222-2-200000000000000000000000000000000
χ4022222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-22-220000000000000000-2-222-2-22200000000000000000000000000000000
χ4122222222-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-22-220000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4222222222-2-2-2-22222-2-22222-2-2-2-2-2-20000000000000000-22-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4322222222-2-2-2-222-2-2-2-2-2-2222222-2-22222-2-2-2-22222-2-2-2-22-22-20000000000000000-2-222-2-22200000000000000000000000000000000
χ4422222222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222222-22-2000000000000000022-2-222-2-200000000000000000000000000000000
χ452222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-20000000000000000-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-222-2-2-2-222-2-20000000000000000-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222000000000000000022-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222000000000000000022-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ492222-2-2-2-2-2-222-2-22222-2-222-2-222-2-200000000000000002-2-2200000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ502222-2-2-2-2-2-222-2-22222-2-222-2-222-2-200000000000000002-2-22000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ512222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-222-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ522222-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-222-20000000000000000-2-22222-2-200000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222220000000000000000-222-200000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ542222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222220000000000000000-222-2000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ552222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2222222-2-2-2-2-2-2-2-222222-2-220000000000000000-2-22222-2-200000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-222-2-22222-2-222-2-222-2-2-2-222222222-2-2-2-22-2-22000000000000000022-2-2-2-22200000000000000000000000000000000
χ5722-2-222-2-22-22-22-2002-2002-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000002i−2i002i−2i002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−20000000000000000
χ5822-2-222-2-22-22-22-2002-2002-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000−2i2i00−2i2i00−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−220000000000000000
χ5922-2-222-2-22-22-22-2002-2002-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000002i−2i002i−2i002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22−22−22−22−220000000000000000
χ6022-2-222-2-22-22-22-2002-2002-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000−2i2i00−2i2i00−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−20000000000000000
χ6122-2-222-2-22-2-22-22002-200-220000-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000002i−2i002i−2i00−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−220000000000000000
χ6222-2-222-2-22-2-22-22002-200-220000-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000−2i2i00−2i2i002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−20000000000000000
χ6322-2-222-2-22-2-22-22002-200-220000-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000002i−2i002i−2i00−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−20000000000000000
χ6422-2-222-2-22-2-22-22002-200-220000-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000−2i2i00−2i2i002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−220000000000000000
χ6522-2-222-2-2-222-2-2200-2200-2200002-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002-2002-2002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ6622-2-222-2-2-222-2-2200-2200-2200002-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000-2200-2200-2200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ6722-2-222-2-2-222-2-2200-2200-2200002-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002-2002-2002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ6822-2-222-2-2-222-2-2200-2200-2200002-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000-2200-2200-2200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ6922-2-222-2-2-22-222-200-22002-20000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002-2002-200-2200-2200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7022-2-222-2-2-22-222-200-22002-20000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000-2200-22002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ7122-2-222-2-2-22-222-200-22002-20000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002-2002-200-2200-2200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ7222-2-222-2-2-22-222-200-22002-20000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000-2200-22002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7322-2-2-2-2222-22-22-200-2200-220000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000002-200-22002-200-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ7422-2-2-2-2222-22-22-200-2200-220000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000-22002-200-22002-2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
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χ994-4-444i−4i−4i4i000000−4i4i00-440000000022−22−2222−2i22i22i2−2i2−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000000000000000000000000
χ1004-4-444i−4i−4i4i000000−4i4i00-4400000000−222222−222i2−2i2−2i22i22i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000000000000000000000000
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χ1024-4-44−4i4i4i−4i0000004i−4i00-4400000000−222222−22−2i22i22i2−2i2−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000000000000000000000000
χ1034-4-44−4i4i4i−4i000000−4i4i004-40000000022−22−2222−2i22i22i2−2i22i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000000000000000000000000
χ1044-4-44−4i4i4i−4i000000−4i4i004-400000000−222222−222i2−2i2−2i22i2−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000000000000000000000000

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