Finite Group Databasebeta

← Group #10690900

Character table — Group #10690900

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122222222222222222223444466666661212121212121212444444666666666666121212121212121212121212888888882424242424242424242424242424242444444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1
χ6111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111
χ7111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111
χ8111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1
χ911111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ1011111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ1111111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ1211111111-1-1-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ1311111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ1822222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1922222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2022222222222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ2122222222222222222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ23222222222222-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ24222222222222-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111111111111111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ25222222222222-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ26222222222222-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2722222222-2-2-2-22222-2-2-2-222222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ2922222222-2-2-2-22222-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111111111-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3022222222-2-2-2-22222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ3122222222-2-2-2-22222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ3222222222-2-2-2-2-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222222200000000000000000000000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-22222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ3422222222-2-2-2-2-2-2-2-22222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2222211111111-1-1-1-11111-1-1-1-1-1-1-1-10000000033−3−3−3−333−3−33333−3−300000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2222211111111-1-1-1-11111-1-1-1-1-1-1-1-100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ372222-2-2-2-222-2-222-2-222-2-220000222-2-2-2-20000000000000022-2-222-2-222-2-20000000000002−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ382222-2-2-2-222-2-222-2-222-2-220000222-2-2-2-20000000000000022-2-222-2-222-2-2000000000000−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ392222-2-2-2-222-2-222-2-222-2-2-10000-1-1-111113333−3−3−3−3000000-1-111-1-111-1-11133−3−333−3−333−3−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ402222-2-2-2-222-2-222-2-222-2-2-10000-1-1-111113333−3−3−3−3000000-1-111-1-111-1-11133−3−333−3−333−3−3−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ412222-2-2-2-222-2-222-2-222-2-2-10000-1-1-11111−3−3−3−33333000000-1-111-1-111-1-111−3−333−3−333−3−3332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ422222-2-2-2-222-2-222-2-222-2-2-10000-1-1-11111−3−3−3−33333000000-1-111-1-111-1-111−3−333−3−333−3−333−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ432222-2-2-2-222-2-2-2-222-2-22220000222-2-2-2-20000000000000022-2-2-2-222-2-222000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ442222-2-2-2-222-2-2-2-222-2-22220000222-2-2-2-20000000000000022-2-2-2-222-2-222000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ452222-2-2-2-222-2-2-2-222-2-222-10000-1-1-111113333−3−3−3−3000000-1-11111-1-111-1-1−3−333−3−33333−3−3−i2i2−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ462222-2-2-2-222-2-2-2-222-2-222-10000-1-1-111113333−3−3−3−3000000-1-11111-1-111-1-1−3−333−3−33333−3−3i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
χ472222-2-2-2-222-2-2-2-222-2-222-10000-1-1-11111−3−3−3−33333000000-1-11111-1-111-1-133−3−333−3−3−3−333−i2i2−i2i2i2−i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000
χ482222-2-2-2-222-2-2-2-222-2-222-10000-1-1-11111−3−3−3−33333000000-1-11111-1-111-1-133−3−333−3−3−3−333i2−i2i2−i2−i2i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
χ492222-2-2-2-2-2-22222-2-2-2-22220000222-2-2-2-200000000000000-2-22222-2-2-2-222000000000000−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ502222-2-2-2-2-2-22222-2-2-2-22220000222-2-2-2-200000000000000-2-22222-2-2-2-222000000000000i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ512222-2-2-2-2-2-22222-2-2-2-222-10000-1-1-111113333−3−3−3−300000011-1-1-1-11111-1-1−3−33333−3−3−3−333−i2i2i2−i2−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ522222-2-2-2-2-2-22222-2-2-2-222-10000-1-1-111113333−3−3−3−300000011-1-1-1-11111-1-1−3−33333−3−3−3−333i2−i2−i2i2i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
χ532222-2-2-2-2-2-22222-2-2-2-222-10000-1-1-11111−3−3−3−3333300000011-1-1-1-11111-1-133−3−3−3−33333−3−3−i2i2i2−i2−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000
χ542222-2-2-2-2-2-22222-2-2-2-222-10000-1-1-11111−3−3−3−3333300000011-1-1-1-11111-1-133−3−3−3−33333−3−3i2−i2−i2i2i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
χ552222-2-2-2-2-2-222-2-22222-2-220000222-2-2-2-200000000000000-2-222-2-22222-2-20000000000002−2−22−222−22−22−2−22−22−22−222−22−200000000000000000000
χ562222-2-2-2-2-2-222-2-22222-2-220000222-2-2-2-200000000000000-2-222-2-22222-2-2000000000000−222−22−2−22−22−222−22−22−22−2−22−2200000000000000000000
χ572222-2-2-2-2-2-222-2-22222-2-2-10000-1-1-111113333−3−3−3−300000011-1-111-1-1-1-11133−3−3−3−333−3−3332−2−22−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ582222-2-2-2-2-2-222-2-22222-2-2-10000-1-1-111113333−3−3−3−300000011-1-111-1-1-1-11133−3−3−3−333−3−333−222−22−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
χ592222-2-2-2-2-2-222-2-22222-2-2-10000-1-1-11111−3−3−3−3333300000011-1-111-1-1-1-111−3−33333−3−333−3−32−2−22−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ602222-2-2-2-2-2-222-2-22222-2-2-10000-1-1-11111−3−3−3−3333300000011-1-111-1-1-1-111−3−33333−3−333−3−3−222−22−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ6122-2-222-2-200002-22-2000022i2i−2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i002i−2i0000002-22-2000000002i−2i2i−2i00000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000
χ6222-2-222-2-200002-22-2000022i2i−2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i002i−2i0000002-22-2000000002i−2i2i−2i0000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.