Finite Group Databasebeta

← Group #197589

Character table — Group #197589

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12224444222244444444444444448888888888888888222224444444444444448888888888888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-111-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-111-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-111
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ171111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-111111-1111-1-1-1-111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−ii−ii−i1-11-1
χ181111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-111111-1111-1-1-1-111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii−ii−ii-11-11
χ191111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-11-11-1-11111-1-11111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−iii−ii−i-11-11
χ201111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-11-11-1-11111-1-11111ii−i−iii−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i−ii−ii1-11-1
χ211111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-111111-1111-1-1-1-111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii−ii−ii1-11-1
χ221111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-111111-1111-1-1-1-111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−ii−ii−i-11-11
χ231111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-11-11-1-11111-1-11111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i−ii−ii-11-11
χ241111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-11-11-1-11111-1-11111−i−iii−i−iiiiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−iii−ii−i1-11-1
χ251111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-11-1-111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−iii−i−ii1-1-11
χ261111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-11-1-111-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i−iii−i-111-1
χ271111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-1111111-1-1-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−ii−i−ii-111-1
χ281111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-1111111-1-1-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii−iii−i1-1-11
χ291111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-11-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i−iii−i1-1-11
χ301111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-11-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−iii−i−ii-111-1
χ311111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-1111111-1-1-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii−iii−i-111-1
χ321111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-1111111-1-1-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−ii−i−ii1-1-11
χ33222222222222-2-2-2-2-2-222-2-2-2-222-2-2000000000000000022222-2-22-2-222-2-2-2-222-2-20000000000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-222-2-2-2-222-2-200000000000000002-2-2-2-2-2-2222-2-22222-2-2220000000000000000000000000000000000000000
χ352222222222-2-22222-2-22222-2-2-2-2222222222222222222-20000-2-2-2000000000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ362222222222-2-22222-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-2-2-20000000000002222222200000000000000000000000000000000
χ372222222222-2-2-2-2-2-22222-2-222-2-2-2-20000000000000000-2000022-2000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ382222222222-2-2-2-2-2-22222-2-222-2-2-2-20000000000000000-2000022-200000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-222-2-22222-2-2222222-2-20000000000000000-222-2-2-2-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000
χ4022222222-2-222-2-22222-2-2222222-2-20000000000000000-2-2-222-2-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ4122222222-2-2-2-222-2-222-2-2-2-222-2-22222222222-2-2-2-2-2-2-2-220000-2-22000000000000-2-2-2-2222200000000000000000000000000000000
χ4222222222-2-2-2-222-2-222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222222220000-2-220000000000002222-2-2-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2000000000000000020000222000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4422222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-200000000000000002000022200000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ452222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i20000-22-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i20000-22-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2220000000000000000200002-2-20000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ482222-2-2-2-22222-2-2-2-222-2-222-2-2-2-2220000000000000000200002-2-200000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ492222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000-22222-222-2-2-2-222-2-2-2-2220000000000000000000000000000000000000000
χ502222-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2-2-2222222-2-22222-2-20000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-20000-222000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ522222-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-20000-2220000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-222-2-222-2-222-2-2220000000000000000-200002-220000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ542222-2-2-2-2-2-222-2-222-2-222-2-222-2-2220000000000000000-200002-2200000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ552222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222220000000000000000222-2-2-22-2-2-2-2-2222222-2-20000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2222200000000000000002-2-222-22-22222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ5722-2-222-2-2002-2002i−2i2i−2i002i−2i2i−2i2-200i2i2−i2−i2i2i2−i2−i222−2−222−2−20002-20002i−2i002i−2i002-200i2−i2i2−i22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ5822-2-222-2-2002-2002i−2i2i−2i002i−2i2i−2i2-200i2i2−i2−i2i2i2−i2−i222−2−222−2−2000-22000−2i2i00−2i2i00-2200i2−i2i2−i22−22−2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ5922-2-222-2-2002-2002i−2i2i−2i002i−2i2i−2i2-200−i2−i2i2i2−i2−i2i2i2−2−222−2−2220002-20002i−2i002i−2i002-200−i2i2−i2i2−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ6022-2-222-2-2002-2002i−2i2i−2i002i−2i2i−2i2-200−i2−i2i2i2−i2−i2i2i2−2−222−2−222000-22000−2i2i00−2i2i00-2200−i2i2−i2i2−22−222−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ6122-2-222-2-2002-200−2i2i−2i2i00−2i2i−2i2i2-200i2i2−i2−i2i2i2−i2−i2−2−222−2−2220002-2000−2i2i00−2i2i002-200i2−i2i2−i2−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ6222-2-222-2-2002-200−2i2i−2i2i00−2i2i−2i2i2-200i2i2−i2−i2i2i2−i2−i2−2−222−2−222000-220002i−2i002i−2i00-2200i2−i2i2−i2−22−222−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6322-2-222-2-2002-200−2i2i−2i2i00−2i2i−2i2i2-200−i2−i2i2i2−i2−i2i2i222−2−222−2−20002-2000−2i2i00−2i2i002-200−i2i2−i2i22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6422-2-222-2-2002-200−2i2i−2i2i00−2i2i−2i2i2-200−i2−i2i2i2−i2−i2i2i222−2−222−2−2000-220002i−2i002i−2i00-2200−i2i2−i2i22−22−2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ6522-2-222-2-200-22002i−2i−2i2i002i−2i−2i2i-2200i2i2−i2−i2i2i2−i2−i222−2−222−2−202-200000002-2002i−2i002i−2i−i2i2−i2i2−22−22i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ6622-2-222-2-200-22002i−2i−2i2i002i−2i−2i2i-2200i2i2−i2−i2i2i2−i2−i222−2−222−2−20-220000000-2200−2i2i00−2i2i−i2i2−i2i2−22−22−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ6722-2-222-2-200-22002i−2i−2i2i002i−2i−2i2i-2200−i2−i2i2i2−i2−i2i2i2−2−222−2−22202-200000002-2002i−2i002i−2ii2−i2i2−i22−22−2−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000000000
χ6822-2-222-2-200-22002i−2i−2i2i002i−2i−2i2i-2200−i2−i2i2i2−i2−i2i2i2−2−222−2−2220-220000000-2200−2i2i00−2i2ii2−i2i2−i22−22−2i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000000000
χ6922-2-222-2-200-2200−2i2i2i−2i00−2i2i2i−2i-2200i2i2−i2−i2i2i2−i2−i2−2−222−2−22202-200000002-200−2i2i00−2i2i−i2i2−i2i22−22−2i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ7022-2-222-2-200-2200−2i2i2i−2i00−2i2i2i−2i-2200i2i2−i2−i2i2i2−i2−i2−2−222−2−2220-220000000-22002i−2i002i−2i−i2i2−i2i22−22−2−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ7122-2-222-2-200-2200−2i2i2i−2i00−2i2i2i−2i-2200−i2−i2i2i2−i2−i2i2i222−2−222−2−202-200000002-200−2i2i00−2i2ii2−i2i2−i2−22−22−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000000000
χ7222-2-222-2-200-2200−2i2i2i−2i00−2i2i2i−2i-2200−i2−i2i2i2−i2−i2i2i222−2−222−2−20-220000000-22002i−2i002i−2ii2−i2i2−i2−22−22i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000000000
χ7322-2-2-2-222002-2002i−2i−2i2i00−2i2i2i−2i-220022−2−2−2−222−i2−i2i2i2i2i2−i2−i202-20000000-22002i−2i00−2i2i−222−2i2−i2−i2i22−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ7422-2-2-2-222002-2002i−2i−2i2i00−2i2i2i−2i-220022−2−2−2−222−i2−i2i2i2i2i2−i2−i20-2200000002-200−2i2i002i−2i−222−2i2−i2−i2i2−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
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χ894-44-44i−4i4i−4i00004-40000000000004i−4i000000004ζ−4ζ4ζ−4ζ4ζ3−4ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000
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χ1044-4-44−4i4i4i−4i-44000000004i−4i00000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.