Finite Group Databasebeta

← Group #10693430

Character table — Group #10693430

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12224444223444444444466612121212121212121212121266888888881212121212122424242424242424242424242424242488888888242424242424242424242424242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii−ii-1-111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii−ii-1-111−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−ii−i-1-111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i-1-111
χ141111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−ii−i-1-111iiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii11-1-1
χ151111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii−ii11-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii11-1-1
χ161111-1-1-1-1111-1-111-1-111-1-11111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii−ii11-1-1−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i-1-111
χ172222222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-22200000000-2-222-2-2000000000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-22200000000-2-222-2-200000000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-122-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-11111-1-10000000011-1-1113333−3−3−3−33333−3−3−3−300002i−2i2i−2i−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000000000000000
χ242222222222-122-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-11111-1-10000000011-1-1113333−3−3−3−33333−3−3−3−30000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000000000000000
χ252222222222-122-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-11111-1-10000000011-1-111−3−3−3−33333−3−3−3−3333300002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii0000000000000000
χ262222222222-122-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-11111-1-10000000011-1-111−3−3−3−33333−3−3−3−333330000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i0000000000000000
χ2722222222-2-22-2-22222-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ2822222222-2-22-2-22222-2-2-2-2222222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ2922222222-2-22-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-20000000022-2-222000000000000000022-2-200002-22-22-22-2000000000000000000000000
χ3022222222-2-22-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-20000000022-2-2220000000000000000-2-2220000-22-22-22-22000000000000000000000000
χ3122222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11122-2-222-2-2111111-1-111-1-111-1-111-1-11100000000−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3222222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11122-2-222-2-2111111-1-111-1-111-1-111-1-11100000000i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3322222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-2-222-2-22211111111-1-111-1-111-1-111-1-100000000−i3i3i3−i3−i3i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3422222222-2-2-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-2-222-2-22211111111-1-111-1-111-1-111-1-100000000i3−i3−i3i3i3−i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3522222222-2-2-1-2-2-2-2-2-22222-1-1-11111-1-1-1-111111100000000-1-111-1-133−3−3−3−33333−3−3−3−33322-2-20000-11-11-11-113−3−333−3−330000000000000000
χ3622222222-2-2-1-2-2-2-2-2-22222-1-1-11111-1-1-1-111111100000000-1-111-1-133−3−3−3−33333−3−3−3−333-2-22200001-11-11-11-1−333−3−333−30000000000000000
χ3722222222-2-2-1-2-2-2-2-2-22222-1-1-11111-1-1-1-111111100000000-1-111-1-1−3−33333−3−3−3−33333−3−322-2-20000-11-11-11-11−333−3−333−30000000000000000
χ3822222222-2-2-1-2-2-2-2-2-22222-1-1-11111-1-1-1-111111100000000-1-111-1-1−3−33333−3−3−3−33333−3−3-2-22200001-11-11-11-13−3−333−3−330000000000000000
χ392222-2-2-2-2222-2-2-2-222-2-222222-2-2-2-2-2-2-2-222222200000000-2-2-2-222000000000000000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2222-2-2-2-222-2-222222-2-2-2-2-2-2-2-222222200000000-2-2-2-22200000000000000000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-222-1-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-12i2i2i2i−2i−2i−2i−2i-1-11111−i−i−i−i−i−i−i−iiiiiiiii2i−2i2i−2i22-2-2−i−i−i−iiiii-1-1-1-111110000000000000000
χ422222-2-2-2-222-1-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-12i2i2i2i−2i−2i−2i−2i-1-11111−i−i−i−i−i−i−i−iiiiiiiii−2i2i−2i2i-2-222iiii−i−i−i−i1111-1-1-1-10000000000000000
χ432222-2-2-2-222-1-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-1−2i−2i−2i−2i2i2i2i2i-1-11111iiiiiiii−i−i−i−i−i−i−i−i2i−2i2i−2i-2-222−i−i−i−iiiii1111-1-1-1-10000000000000000
χ442222-2-2-2-222-1-2-222-2-222-2-2-1-1-1-1-1-1-111111111-1-1−2i−2i−2i−2i2i2i2i2i-1-11111iiiiiiii−i−i−i−i−i−i−i−i−2i2i−2i2i22-2-2iiii−i−i−i−i-1-1-1-111110000000000000000
χ452222-2-2-2-222-1-2-2-2-222-2-222-1-1-111111111-1-1-1-1-1-1000000001111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300002i−2i−2i2i−3−33333−3−3−i−iiiii−i−i0000000000000000
χ462222-2-2-2-222-1-2-2-2-222-2-222-1-1-111111111-1-1-1-1-1-1000000001111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000−2i2i2i−2i33−3−3−3−333ii−i−i−i−iii0000000000000000
χ472222-2-2-2-222-1-2-2-2-222-2-222-1-1-111111111-1-1-1-1-1-1000000001111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300002i−2i−2i2i33−3−3−3−333−i−iiiii−i−i0000000000000000
χ482222-2-2-2-222-1-2-2-2-222-2-222-1-1-111111111-1-1-1-1-1-1000000001111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000−2i2i2i−2i−3−33333−3−3ii−i−i−i−iii0000000000000000
χ492222-2-2-2-2-2-222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-2-2-222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-2-2-22222-2-2000000002222-2-200000000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ522222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-2-2-22222-2-2000000002222-2-20000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ532222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1-1-1-1-111111111112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−iii−i−iiiii−i−iii−i−i000000003−3−33−333−3−i3i3−i3i3i3−i3i3−i30000000000000000
χ542222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1-1-1-1-111111111112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−iii−i−iiiii−i−iii−i−i00000000−333−33−3−33i3−i3i3−i3−i3i3−i3i30000000000000000
χ552222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1-1-1-1-11111111111−2i−2i2i2i2i2i−2i−2i11-1-1-1-1ii−i−iii−i−i−i−iii−i−iii000000003−3−33−333−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ562222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1-1-1-1-11111111111−2i−2i2i2i2i2i−2i−2i11-1-1-1-1ii−i−iii−i−i−i−iii−i−iii00000000−333−33−3−33−i3i3−i3i3i3−i3i3−i30000000000000000
χ572222-2-2-2-2-2-2-122-2-22222-2-2-1-1-111111111-1-1-1-11100000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32i−2i−2i2i0000−ii−iii−ii−i−333−33−3−330000000000000000
χ582222-2-2-2-2-2-2-122-2-22222-2-2-1-1-111111111-1-1-1-11100000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−2i2i2i−2i0000i−ii−i−ii−ii3−3−33−333−30000000000000000
χ592222-2-2-2-2-2-2-122-2-22222-2-2-1-1-111111111-1-1-1-11100000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32i−2i−2i2i0000−ii−iii−ii−i3−3−33−333−30000000000000000
χ602222-2-2-2-2-2-2-122-2-22222-2-2-1-1-111111111-1-1-1-11100000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−2i2i2i−2i0000i−ii−i−ii−ii−333−33−3−330000000000000000
χ612-22-22i−2i2i−2i2-222i−2i2-22i−2i2-22i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i2-2000000002-22i−2i2i−2i00000000000000000000000000000000000000000000000000002i−2i2-2
χ622-22-22i−2i2i−2i2-222i−2i2-22i−2i2-22i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i2-2000000002-22i−2i2i−2i0000000000000000000000000000000000000000000000000000−2i2i-22
χ632-22-22i−2i2i−2i2-222i−2i-22−2i2i-22−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-200000000-222i−2i−2i2i00000000000000000000000000000000000000002-22i−2i000000000000
χ642-22-22i−2i2i−2i2-222i−2i-22−2i2i-22−2i2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i2-200000000-222i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i000000000000
χ652-22-22i−2i2i−2i-222−2i2i2-22i−2i-22−2i2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i-2200000000-22−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ662-22-22i−2i2i−2i-222−2i2i2-22i−2i-22−2i2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i-2200000000-22−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ672-22-22i−2i2i−2i-222−2i2i-22−2i2i2-22i−2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22000000002-2−2i2i2i−2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ682-22-22i−2i2i−2i-222−2i2i-22−2i2i2-22i−2i2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22000000002-2−2i2i2i−2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ692-22-2−2i2i−2i2i2-22−2i2i2-2−2i2i2-2−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-2000000002-2−2i2i−2i2i00000000000000000000000000000000000000000000000000002i−2i-22
χ702-22-2−2i2i−2i2i2-22−2i2i2-2−2i2i2-2−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i2-2000000002-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000−2i2i2-2
χ712-22-2−2i2i−2i2i2-22−2i2i-222i−2i-222i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-200000000-22−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i000000000000
χ722-22-2−2i2i−2i2i2-22−2i2i-222i−2i-222i−2i2-2-2-2-222−2i−2i2i2i2i2i−2i−2i2-200000000-22−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i000000000000
χ732-22-2−2i2i−2i2i-2222i−2i2-2−2i2i-222i−2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2200000000-222i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ742-22-2−2i2i−2i2i-2222i−2i2-2−2i2i-222i−2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2200000000-222i−2i2i−2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
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χ974-4-444i−4i−4i4i0040000000000-4-4400004i−4i−4i4i0000002−2i−2+2i002+2i−2−2i000000002−2i−2+2i002−2i−2+2i002+2i−2−2i002+2i−2−2i000000000000000000000000000000000000000000
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χ1064-4-44−4i4i4i−4i00-2000000000022-223−23−23232i−2i−2i2i−2i32i32i3−2i300−2−2i2+2i00−2+2i2−2i000000002ζ20−2ζ22−2ζ20+2ζ22002ζ4−2ζ14−2ζ4+2ζ14002ζ4+2ζ14−2ζ4−2ζ14002ζ20+2ζ22−2ζ20−2ζ22000000000000000000000000000000000000000000
χ1074-4-44−4i4i4i−4i00-2000000000022-2−232323−232i−2i−2i2i2i3−2i3−2i32i3002+2i−2−2i002−2i−2+2i00000000−2ζ4+2ζ142ζ4−2ζ1400−2ζ20+2ζ222ζ20−2ζ2200−2ζ20−2ζ222ζ20+2ζ2200−2ζ4−2ζ142ζ4+2ζ14000000000000000000000000000000000000000000
χ1084-4-44−4i4i4i−4i00-2000000000022-2−232323−232i−2i−2i2i2i3−2i3−2i32i300−2−2i2+2i00−2+2i2−2i000000002ζ4−2ζ14−2ζ4+2ζ14002ζ20−2ζ22−2ζ20+2ζ22002ζ20+2ζ22−2ζ20−2ζ22002ζ4+2ζ14−2ζ4−2ζ14000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.