Finite Group Databasebeta

← Group #110946

Character table — Group #110946

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222224444444444444444444444444444444444444444444444444444444444444444442444888888888888
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
χ911111-1-1-11-11111-1-111-1-1-1-1111-1-1-1iiiiiiii−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
χ1011111-1-1-11-11111-1-111-1-1-1-1111-1-1-1iiiiiiii−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
χ1111111-1-1-11-11111-1-111-1-1-1-1111-1-1-1iiiiiiii−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
χ1211111-1-1-11-11111-1-111-1-1-1-1111-1-1-1iiiiiiii−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
χ1311111-1-1-11-11111-1-111-1-1-1-1111-1-1-1−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
χ1411111-1-1-11-11111-1-111-1-1-1-1111-1-1-1−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
χ1511111-1-1-11-11111-1-111-1-1-1-1111-1-1-1−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
χ1611111-1-1-11-11111-1-111-1-1-1-1111-1-1-1−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
χ171111-11-1-1-1111-1-111-1-111-1-111-11-1-1iiii−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
χ181111-11-1-1-1111-1-111-1-111-1-111-11-1-1iiii−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
χ191111-11-1-1-1111-1-111-1-111-1-111-11-1-1iiii−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
χ201111-11-1-1-1111-1-111-1-111-1-111-11-1-1iiii−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
χ211111-11-1-1-1111-1-111-1-111-1-111-11-1-1−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
χ221111-11-1-1-1111-1-111-1-111-1-111-11-1-1−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
χ231111-11-1-1-1111-1-111-1-111-1-111-11-1-1−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
χ241111-11-1-1-1111-1-111-1-111-1-111-11-1-1−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
χ251111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11i−i−ii−iii−i
χ261111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1−iii−ii−i−ii
χ271111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11−iii−ii−i−ii
χ281111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1i−i−ii−iii−i
χ291111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1i−i−iii−i−ii
χ301111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11−iii−i−iii−i
χ311111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1−iii−i−iii−i
χ321111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11i−i−iii−i−ii
χ33222222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222-2-222-2-2-2-222-2-22-2-2-22-20000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ362222222222-2-222-2-2-2-222-2-22-2-2-22-200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ372222222222-2-2-2-22222-2-2-2-2-22-2-2-22000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ382222222222-2-2-2-22222-2-2-2-2-22-2-2-220000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ3922222-2-2-22-222-2-222-2-222-2-2-2-22-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4022222-2-2-22-222-2-222-2-222-2-2-2-22-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4122222-2-2-22-2-2-22222-2-2-2-2222-2-22-22000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ4222222-2-2-22-2-2-22222-2-2-2-2222-2-22-2200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ4322222-2-2-22-2-2-2-2-2-2-2222222-22-222-2000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4422222-2-2-22-2-2-2-2-2-2-2222222-22-222-20000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ452222-22-2-2-222222-2-222-2-2-2-2-2-2-22222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ462222-22-2-2-222222-2-222-2-2-2-2-2-2-2222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ472222-22-2-2-22-2-22222-2-2-2-222-222-22-200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ482222-22-2-2-22-2-22222-2-2-2-222-222-22-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ492222-22-2-2-22-2-2-2-2-2-22222222-22-2-220000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ502222-22-2-2-22-2-2-2-2-2-22222222-22-2-2200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ512222-2-222-2-2222222222222-2-2-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ522222-2-222-2-2222222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ532222-2-222-2-2-2-222-2-2-2-222-2-2-2222-2200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ542222-2-222-2-2-2-222-2-2-2-222-2-2-2222-220000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ552222-2-222-2-2-2-2-2-22222-2-2-2-22-2222-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ562222-2-222-2-2-2-2-2-22222-2-2-2-22-2222-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ5722-2-2002-2002-22i−2i2i−2i2i−2i2i−2i2-2000000002i−2i2-2002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ5822-2-2002-2002-22i−2i2i−2i2i−2i2i−2i2-2000000002i−2i2-2002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ5922-2-2002-2002-22i−2i2i−2i2i−2i2i−2i2-200000000−2i2i-2200-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ6022-2-2002-2002-22i−2i2i−2i2i−2i2i−2i2-200000000−2i2i-2200-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ6122-2-2002-2002-2−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i-2200-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6222-2-2002-2002-2−2i2i−2i2i−2i2i−2i2i2-2000000002i−2i-2200-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6322-2-2002-2002-2−2i2i−2i2i−2i2i−2i2i2-200000000−2i2i2-2002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ6422-2-2002-2002-2−2i2i−2i2i−2i2i−2i2i2-200000000−2i2i2-2002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6522-2-2002-200-222i−2i−2i2i−2i2i2i−2i-220000002-200002i−2i002i−2i2-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ6622-2-2002-200-222i−2i−2i2i−2i2i2i−2i-220000002-200002i−2i002i−2i2-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ6722-2-2002-200-222i−2i−2i2i−2i2i2i−2i-22000000-220000−2i2i00−2i2i-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ6822-2-2002-200-222i−2i−2i2i−2i2i2i−2i-22000000-220000−2i2i00−2i2i-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ6922-2-2002-200-22−2i2i2i−2i2i−2i−2i2i-220000002-20000−2i2i00−2i2i2-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ7022-2-2002-200-22−2i2i2i−2i2i−2i−2i2i-220000002-20000−2i2i00−2i2i2-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ7122-2-2002-200-22−2i2i2i−2i2i−2i−2i2i-22000000-2200002i−2i002i−2i-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ7222-2-2002-200-22−2i2i2i−2i2i−2i−2i2i-22000000-2200002i−2i002i−2i-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ7322-2-200-22002-22i−2i−2i2i2i−2i−2i2i-22000000002-2−2i2i002i−2i0000-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000000000000000
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χ7522-2-200-22002-22i−2i−2i2i2i−2i−2i2i-2200000000-222i−2i00−2i2i00002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000000000000000
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χ8722-2-200-2200-22−2i2i−2i2i2i−2i2i−2i2-2000000−2i2i0000-22002-22i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
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χ898-88-808000-80000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-80-800080000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-888000-800000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-8000800000000000000000000000000000000000000000000000000000000000000000000000000000000000

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