Finite Group Databasebeta

← Group #10702260

Character table — Group #10702260

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222222244444444222234444666666612121212121212126666888888881212121224242424242424242424242424242424224466668888121212122424242424242424444444448888888844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ1722222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ1822222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000000000000000
χ1922222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000000000
χ2022222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-2-2-2-22-2-2-2-2222222222222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ222222222222222222-2-2-2-22-2-2-2-2222222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ232222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122-2-222-2-21111-1-1-1-11111-1-1-1-111110000−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111122-2-222-2-21111-1-1-1-11111-1-1-1-111110000i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-22211111111-1-1-1-11111-1-1-1-10000−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-22211111111-1-1-1-11111-1-1-1-10000i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i1111−i−i−i−iiiiiiiii−i−i−i−i0000−i3−i3i3i30000i3i3−i3−i333−3−3−3−333000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i1111−i−i−i−iiiiiiiii−i−i−i−i0000i3i3−i3−i30000−i3−i3i3i3−3−33333−3−3000000000000000000000000
χ3122222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i1111iiii−i−i−i−i−i−i−i−iiiii0000−i3−i3i3i30000i3i3−i3−i3−3−33333−3−3000000000000000000000000
χ3222222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i1111iiii−i−i−i−i−i−i−i−iiiii0000i3i3−i3−i30000−i3−i3i3i333−3−3−3−333000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii000000000000000000000000
χ3422222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ37222-2-22-2-22222-2-2-2-222-2-2222-2-222-2-2-2-222222-2-2-2-222-2-20000000022-2-200000000000000002-22-22-22-200002-22-200000000000000000000000000000000
χ38222-2-22-2-22222-2-2-2-222-2-2222-2-222-2-2-2-222222-2-2-2-222-2-20000000022-2-20000000000000000-22-22-22-220000-22-2200000000000000000000000000000000
χ39222-2-22-2-22222-2-2-2-222-2-2-122-2-2-1-11111-1-1-1-1-11111-1-11100000000-1-11133−3−333−3−333−3−333−3−32-22-2-11-110000-11-113−33−33−33−3000000000000000000000000
χ40222-2-22-2-22222-2-2-2-222-2-2-122-2-2-1-11111-1-1-1-1-11111-1-11100000000-1-11133−3−333−3−333−3−333−3−3-22-221-11-100001-11-1−33−33−33−33000000000000000000000000
χ41222-2-22-2-22222-2-2-2-222-2-2-122-2-2-1-11111-1-1-1-1-11111-1-11100000000-1-111−3−333−3−333−3−333−3−3332-22-2-11-110000-11-11−33−33−33−33000000000000000000000000
χ42222-2-22-2-22222-2-2-2-222-2-2-122-2-2-1-11111-1-1-1-1-11111-1-11100000000-1-111−3−333−3−333−3−333−3−333-22-221-11-100001-11-13−33−33−33−3000000000000000000000000
χ43222-2-22-2-22222-2-2-2-2-2-2222-2-22222-2-2-2-222222-2-2-2-2-2-22200000000-2-2220000000000000000000000002i−2i2i−2i00002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ44222-2-22-2-22222-2-2-2-2-2-2222-2-22222-2-2-2-222222-2-2-2-2-2-22200000000-2-222000000000000000000000000−2i2i−2i2i0000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ45222-2-22-2-22222-2-2-2-2-2-222-1-2-222-1-11111-1-1-1-1-1111111-1-10000000011-1-133−3−3−3−33333−3−3−3−3330000−i3i3i3−i32i−2i2i−2i−i3i3i3−i3−iii−i−iii−i000000000000000000000000
χ46222-2-22-2-22222-2-2-2-2-2-222-1-2-222-1-11111-1-1-1-1-1111111-1-10000000011-1-133−3−3−3−33333−3−3−3−3330000i3−i3−i3i3−2i2i−2i2ii3−i3−i3i3i−i−iii−i−ii000000000000000000000000
χ47222-2-22-2-22222-2-2-2-2-2-222-1-2-222-1-11111-1-1-1-1-1111111-1-10000000011-1-1−3−33333−3−3−3−33333−3−30000−i3i3i3−i3−2i2i−2i2i−i3i3i3−i3i−i−iii−i−ii000000000000000000000000
χ48222-2-22-2-22222-2-2-2-2-2-222-1-2-222-1-11111-1-1-1-1-1111111-1-10000000011-1-1−3−33333−3−3−3−33333−3−30000i3−i3−i3i32i−2i2i−2ii3−i3−i3i3−iii−i−iii−i000000000000000000000000
χ49222-2-22-2-2-2-2-2-2222222-2-22-2-22222-2-2-2-22-2-2-2-2222222-2-200000000-2-2220000000000000000000000002-2-2200002-2-22-222-2000000000000000000000000
χ50222-2-22-2-2-2-2-2-2222222-2-22-2-22222-2-2-2-22-2-2-2-2222222-2-200000000-2-222000000000000000000000000-222-20000-222-22-2-22000000000000000000000000
χ51222-2-22-2-2-2-2-2-2222222-2-2-1-2-222-1-11111-11111-1-1-1-1-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3i3i3−i32-2-22i3−i3−i3i3-111-11-1-11000000000000000000000000
χ52222-2-22-2-2-2-2-2-2222222-2-2-1-2-222-1-11111-11111-1-1-1-1-1-1110000000011-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3−i3−i3i3-222-2−i3i3i3−i31-1-11-111-1000000000000000000000000
χ53222-2-22-2-2-2-2-2-2222222-2-2-1-2-222-1-11111-11111-1-1-1-1-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−i3i3i3−i3-222-2i3−i3−i3i31-1-11-111-1000000000000000000000000
χ54222-2-22-2-2-2-2-2-2222222-2-2-1-2-222-1-11111-11111-1-1-1-1-1-1110000000011-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000i3−i3−i3i32-2-22−i3i3i3−i3-111-11-1-11000000000000000000000000
χ55222-2-22-2-2-2-2-2-22222-2-222222-2-222-2-2-2-22-2-2-2-22222-2-2220000000022-2-200000000000000002-2-222-22-20000-22-2200000000000000000000000000000000
χ56222-2-22-2-2-2-2-2-22222-2-222222-2-222-2-2-2-22-2-2-2-22222-2-2220000000022-2-20000000000000000-222-2-22-2200002-22-200000000000000000000000000000000
χ57222-2-22-2-2-2-2-2-22222-2-222-122-2-2-1-11111-11111-1-1-1-111-1-100000000-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2-22-11-1100001-11-1−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ58222-2-22-2-2-2-2-2-22222-2-222-122-2-2-1-11111-11111-1-1-1-111-1-100000000-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-222-21-11-10000-11-11i3−i3i3−i3−i3i3−i3i3000000000000000000000000
χ59222-2-22-2-2-2-2-2-22222-2-222-122-2-2-1-11111-11111-1-1-1-111-1-100000000-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-2-22-11-1100001-11-1i3−i3i3−i3−i3i3−i3i3000000000000000000000000
χ60222-2-22-2-2-2-2-2-22222-2-222-122-2-2-1-11111-11111-1-1-1-111-1-100000000-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-222-21-11-10000-11-11−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ6122-22-2-22-22i2i−2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−i2−i2i2i222−2−200000000
χ6222-22-2-22-22i2i−2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−ii2i2−i2−i2−2−22200000000
χ6322-22-2-22-22i2i−2i−2i2i−2i2i−2i0000200002-222-2-2-22i2i−2i−2i2i2i−2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+ii2i2−i2−i2−2−22200000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.