Finite Group Databasebeta

← Group #10703028

Character table — Group #10703028

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121244444444666612121212121212121212121212121212121212122244444466661212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-11-1ii−i−i11-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-11-1ii−i−i11-1-1iiii−i−i−i−i11-1-1-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11-11−i−iii-1-111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11-11−i−iii-1-111−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-11-1−i−iii11-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-11-1−i−iii11-1-1−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11-11ii−i−i-1-111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-1-111
χ161111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11-11ii−i−i-1-111iiii−i−i−i−i-1-111-1-111−i−iiiii−i−i11-1-1
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-1-10000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-2-2-2-222221111-1-1-1-1-1-1-1-111110000000000000000
χ212222222222-2-2-2-22-2-2-222-222-2-2-2-22-2-2-2-222220000000022-2-20000000000000000-2-22200002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ222222222222-2-2-2-22-2-2-222-222-2-2-2-22-2-2-2-222220000000022-2-20000000000000000-2-2220000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ232222222222-2-2-2-2-1-2-2-222-2-1-11111-11111-1-1-1-100000000-1-1113333−3−3−3−33333−3−3−3−311-1-100002i−2i2i−2i−i3i3−i3i3−i−iii−i−iii−i3i3−i3i30000000000000000
χ242222222222-2-2-2-2-1-2-2-222-2-1-11111-11111-1-1-1-100000000-1-1113333−3−3−3−33333−3−3−3−311-1-10000−2i2i−2i2ii3−i3i3−i3ii−i−iii−i−ii3−i3i3−i30000000000000000
χ252222222222-2-2-2-2-1-2-2-222-2-1-11111-11111-1-1-1-100000000-1-111−3−3−3−33333−3−3−3−3333311-1-100002i−2i2i−2ii3−i3i3−i3−i−iii−i−iiii3−i3i3−i30000000000000000
χ262222222222-2-2-2-2-1-2-2-222-2-1-11111-11111-1-1-1-100000000-1-111−3−3−3−33333−3−3−3−3333311-1-10000−2i2i−2i2i−i3i3−i3i3ii−i−iii−i−i−i3i3−i3i30000000000000000
χ2722222222-2-22-2-2222-2-2-2-2222-2-2-2-22-2-2-2-2222200000000-2-222000000000000000022-2-22-2-22000022-2-200000000-2-2220000000000000000
χ2822222222-2-22-2-2222-2-2-2-2222-2-2-2-22-2-2-2-2222200000000-2-222000000000000000022-2-2-222-20000-2-2220000000022-2-20000000000000000
χ2922222222-2-22-2-22-12-2-2-2-22-1-11111-11111-1-1-1-10000000011-1-133−3−333−3−333−3−333−3−3-1-1112-2-220000-1-1113−33−33−33−311-1-10000000000000000
χ3022222222-2-22-2-22-12-2-2-2-22-1-11111-11111-1-1-1-10000000011-1-133−3−333−3−333−3−333−3−3-1-111-222-2000011-1-1−33−33−33−33-1-1110000000000000000
χ3122222222-2-22-2-22-12-2-2-2-22-1-11111-11111-1-1-1-10000000011-1-1−3−333−3−333−3−333−3−333-1-1112-2-220000-1-111−33−33−33−3311-1-10000000000000000
χ3222222222-2-22-2-22-12-2-2-2-22-1-11111-11111-1-1-1-10000000011-1-1−3−333−3−333−3−333−3−333-1-111-222-2000011-1-13−33−33−33−3-1-1110000000000000000
χ3322222222-2-2-222-22-222-2-2-222222222222222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222-2-2-2-20000000000000000000000000000000000000000
χ3422222222-2-2-222-22-222-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000
χ3522222222-2-2-222-2-1-222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-11111-1-1111100000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000000000
χ3622222222-2-2-222-2-1-222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-11111-1-1111100000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000000000
χ3722222222-2-2-222-2-1-222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111-1-1-1-11111-1-1-1-111111100000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ3822222222-2-2-222-2-1-222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111-1-1-1-11111-1-1-1-111111100000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ392222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-20000000022220000000000000000-2-2-2-200002-2-22000022-2-2-2-22200000000000000000000
χ402222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-20000000022220000000000000000-2-2-2-20000-222-20000-2-22222-2-200000000000000000000
χ412222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3111100002-2-22−i3i3i3−i3-1-11111-1-1−i3i3i3−i30000000000000000
χ422222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i311110000-222-2i3−i3−i3i311-1-1-1-111i3−i3−i3i30000000000000000
χ432222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3111100002-2-22i3−i3−i3i3-1-11111-1-1i3−i3−i3i30000000000000000
χ442222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i311110000-222-2−i3i3i3−i311-1-1-1-111−i3i3i3−i30000000000000000
χ452222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1112-22-22i2i−2i−2i-1-111−i−i−i−iiiii-1-1110000000000000000
χ462222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111-22-22−2i−2i2i2i11-1-1iiii−i−i−i−i11-1-10000000000000000
χ472222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1112-22-2−2i−2i2i2i-1-111iiii−i−i−i−i-1-1110000000000000000
χ482222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111-22-222i2i−2i−2i11-1-1−i−i−i−iiiii11-1-10000000000000000
χ492222-2-2-2-2-2-22-2-222-22222-222-2-2-2-222222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000000000000000000000000000
χ502222-2-2-2-2-2-22-2-222-22222-222-2-2-2-222222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2-2220000000000000000000000000000000000000000
χ512222-2-2-2-2-2-22-2-22-1-22222-2-1-11111-1-1-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-100000000−i3i3−i3i33−3−33−333−3i3−i3i3−i30000000000000000
χ522222-2-2-2-2-2-22-2-22-1-22222-2-1-11111-1-1-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-1−i−iiiii−i−iii−i−i−i−iii11-1-100000000i3−i3i3−i3−333−33−3−33−i3i3−i3i30000000000000000
χ532222-2-2-2-2-2-22-2-22-1-22222-2-1-11111-1-1-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-100000000−i3i3−i3i3−333−33−3−33i3−i3i3−i30000000000000000
χ542222-2-2-2-2-2-22-2-22-1-22222-2-1-11111-1-1-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-100000000i3−i3i3−i33−3−33−333−3−i3i3−i3i30000000000000000
χ552222-2-2-2-2-2-2-222-222-2-22222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000222222-2-20000222200000000-2-2-2-20000000000000000
χ562222-2-2-2-2-2-2-222-222-2-22222222222-2-2-2-2-2-2-2-200000000-2-2-2-200000000000000002222-2-2220000-2-2-2-20000000022220000000000000000
χ572222-2-2-2-2-2-2-222-2-12-2-2222-1-1-1-1-1-1-111111111000000001111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-1-1-122-2-20000-1-1-1-1−i3i3−i3i3i3−i3i3−i311110000000000000000
χ582222-2-2-2-2-2-2-222-2-12-2-2222-1-1-1-1-1-1-111111111000000001111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-1-1-1-2-22200001111i3−i3i3−i3−i3i3−i3i3-1-1-1-10000000000000000
χ592222-2-2-2-2-2-2-222-2-12-2-2222-1-1-1-1-1-1-111111111000000001111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-1-1-122-2-20000-1-1-1-1i3−i3i3−i3−i3i3−i3i311110000000000000000
χ602222-2-2-2-2-2-2-222-2-12-2-2222-1-1-1-1-1-1-111111111000000001111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-1-1-1-2-22200001111−i3i3−i3i3i3−i3i3−i3-1-1-1-10000000000000000
χ6122-2-222-2-22-222-2-22-22-22-22-2-222-2-2222-2-222-2-2000000002-22-200000000000000002-22-2000000000000000000000000000000002i−2i2i−2i0000
χ6222-2-222-2-22-222-2-22-22-22-22-2-222-2-2222-2-222-2-2000000002-22-200000000000000002-22-200000000000000000000000000000000−2i2i−2i2i0000
χ6322-2-222-2-22-2-2-22222-222-2-2-2-2-2-2222-2-22222-2-2000000002-2-220000000000000000-222-20000000000000000000000000000000000002i−2i2i−2i
χ6422-2-222-2-22-2-2-22222-222-2-2-2-2-2-2222-2-22222-2-2000000002-2-220000000000000000-222-2000000000000000000000000000000000000−2i2i−2i2i
χ6522-2-222-2-2-222-22-22-2-22-222-2-2-2-2222-2-22222-2-200000000-222-200000000000000002-2-2200000000000000000000000000002i−2i2i−2i00000000
χ6622-2-222-2-2-222-22-22-2-22-222-2-2-2-2222-2-22222-2-200000000-222-200000000000000002-2-220000000000000000000000000000−2i2i−2i2i00000000
χ6722-2-222-2-2-22-22-22222-2-22-2-2-222-2-2222-2-222-2-200000000-22-220000000000000000-22-220000000000000000000000002i−2i2i−2i000000000000
χ6822-2-222-2-2-22-22-22222-2-22-2-2-222-2-2222-2-222-2-200000000-22-220000000000000000-22-22000000000000000000000000−2i2i−2i2i000000000000
χ6922-2-2-2-2222-222-2-222-22-22-2-2-222-2-22-2-222-2-222000000002-22-20000000000000000-22-220000000000000000000000000000000000002i−2i−2i2i
χ7022-2-2-2-2222-222-2-222-22-22-2-2-222-2-22-2-222-2-222000000002-22-20000000000000000-22-22000000000000000000000000000000000000−2i2i2i−2i
χ7122-2-2-2-2222-2-2-2222-22-2-222-2-2-2-222222-2-2-2-222000000002-2-2200000000000000002-2-22000000000000000000000000000000002-2-220000
χ7222-2-2-2-2222-2-2-2222-22-2-222-2-2-2-222222-2-2-2-222000000002-2-2200000000000000002-2-2200000000000000000000000000000000-222-20000
χ7322-2-2-2-222-222-22-2222-22-2-2-2-2-2-222222-2-2-2-22200000000-222-20000000000000000-222-20000000000000000000000002i−2i−2i2i000000000000
χ7422-2-2-2-222-222-22-2222-22-2-2-2-2-2-222222-2-2-2-22200000000-222-20000000000000000-222-2000000000000000000000000−2i2i2i−2i000000000000
χ7522-2-2-2-222-22-22-222-2-222-22-2-222-2-22-2-222-2-22200000000-22-2200000000000000002-22-200000000000000000000000000002-2-2200000000
χ7622-2-2-2-222-22-22-222-2-222-22-2-222-2-22-2-222-2-22200000000-22-2200000000000000002-22-20000000000000000000000000000-222-200000000
χ7744-4-444-4-44-444-4-4-2-44-44-4422-2-222-2-2-222-2-22200000000-22-220000000000000000-22-220000000000000000000000000000000000000000
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χ1044-4-44−4i4i4i−4i0000004000000-440000-40000−4i4i4i−4i−2+2i2−2i00−2−2i2+2i000000−2+2i2−2i0000−2+2i2−2i−2−2i2+2i0000−2−2i2+2i00000000000000000000000000000000000000000000
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χ1064-4-44−4i4i4i−4i000000-20000002-2−2i32i32i3−2i32−232323−232i−2i−2i2i−2+2i2−2i00−2−2i2+2i0000002ζ10+2ζ11−2ζ10−2ζ1100002ζ2+2ζ7−2ζ2−2ζ72ζ2−2ζ7−2ζ2+2ζ700002ζ10−2ζ11−2ζ10+2ζ1100000000000000000000000000000000000000000000
χ1074-4-44−4i4i4i−4i000000-20000002-22i3−2i3−2i32i3223−23−23232i−2i−2i2i2−2i−2+2i002+2i−2−2i000000−2ζ2−2ζ72ζ2+2ζ70000−2ζ10−2ζ112ζ10+2ζ11−2ζ10+2ζ112ζ10−2ζ110000−2ζ2+2ζ72ζ2−2ζ700000000000000000000000000000000000000000000
χ1084-4-44−4i4i4i−4i000000-20000002-22i3−2i3−2i32i3223−23−23232i−2i−2i2i−2+2i2−2i00−2−2i2+2i0000002ζ2+2ζ7−2ζ2−2ζ700002ζ10+2ζ11−2ζ10−2ζ112ζ10−2ζ11−2ζ10+2ζ1100002ζ2−2ζ7−2ζ2+2ζ700000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.