Finite Group Databasebeta

← Group #10702199

Character table — Group #10702199

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12224444222222344444466666661212121212121212444444446666121212121212121212121212121212121212121244444444121212121212121212121212121212122244444488888888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1−i−iiiii−i−i-1-111
χ121111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1ii−i−i−i−iii-1-111
χ161111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-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
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-2-2-2-22-2-2-222-2-2-2222-2-2-2-2-2-222220000000022-2-2-2-222000000000000000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-22-2-2-222-2-2-2222-2-2-2-2-2-222220000000022-2-2-2-22200000000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232222222222-2-2-2-2-1-2-2-222-211-1-1-1111111-1-1-1-100000000-1-11111-1-13333−3−3−3−33333−3−3−3−300002i−2i2i−2i−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000000000000000
χ242222222222-2-2-2-2-1-2-2-222-211-1-1-1111111-1-1-1-100000000-1-11111-1-13333−3−3−3−33333−3−3−3−30000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000000000000000
χ252222222222-2-2-2-2-1-2-2-222-211-1-1-1111111-1-1-1-100000000-1-11111-1-1−3−3−3−33333−3−3−3−3333300002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii0000000000000000
χ262222222222-2-2-2-2-1-2-2-222-211-1-1-1111111-1-1-1-100000000-1-11111-1-1−3−3−3−33333−3−3−3−333330000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i0000000000000000
χ2722222222-2-22-22-2222-2-2-2-222222222222222222-2-222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000
χ2822222222-2-22-22-2222-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ2922222222-2-22-22-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-111-1-111-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3022222222-2-22-22-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-111-1-111-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3122222222-2-22-22-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111111111-1-111-1-111-1-111-1-100000000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ3222222222-2-22-22-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111111111-1-111-1-111-1-111-1-100000000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ3322222222-2-2-22-222-2-22-2-22-2-2222-2-2-2-2-2-2222200000000-2-22222-2-200000000000000002-22-200002-2-222-2-22000000000000000000000000
χ3422222222-2-2-22-222-2-22-2-22-2-2222-2-2-2-2-2-2222200000000-2-22222-2-20000000000000000-22-220000-222-2-222-2000000000000000000000000
χ3522222222-2-2-22-22-1-2-22-2-2211-1-1-1111111-1-1-1-10000000011-1-1-1-11133−3−3−3−33333−3−3−3−3332-22-20000-111-1-111-13−3−333−3−330000000000000000
χ3622222222-2-2-22-22-1-2-22-2-2211-1-1-1111111-1-1-1-10000000011-1-1-1-11133−3−3−3−33333−3−3−3−333-22-2200001-1-111-1-11−333−3−333−30000000000000000
χ3722222222-2-2-22-22-1-2-22-2-2211-1-1-1111111-1-1-1-10000000011-1-1-1-111−3−33333−3−3−3−33333−3−32-22-20000-111-1-111-1−333−3−333−30000000000000000
χ3822222222-2-2-22-22-1-2-22-2-2211-1-1-1111111-1-1-1-10000000011-1-1-1-111−3−33333−3−3−3−33333−3−3-22-2200001-1-111-1-113−3−333−3−330000000000000000
χ392222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002-2-220000000022-2-2-2-2220000000000000000
χ402222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000-222-200000000-2-22222-2-20000000000000000
χ412222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300002-2-22−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000000000
χ422222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000-222-2i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000000000
χ432222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300002-2-22i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000000000
χ442222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000-222-2−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000000000
χ452222-2-2-2-222-2-2-2-2-1222-2-2211-1-1-111-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
χ462222-2-2-2-222-2-2-2-2-1222-2-2211-1-1-111-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ472222-2-2-2-222-2-2-2-2-1222-2-2211-1-1-111-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ482222-2-2-2-222-2-2-2-2-1222-2-2211-1-1-111-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ492222-2-2-2-2-2-22-22-22-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000002-2-2200002-2-22-222-2000000000000000000000000
χ502222-2-2-2-2-2-22-22-22-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-222-20000-222-22-2-22000000000000000000000000
χ512222-2-2-2-2-2-22-22-2-1-2-22222-1-1-1-1-1-1-111111111000000001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32-2-220000-111-11-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ522222-2-2-2-2-2-22-22-2-1-2-22222-1-1-1-1-1-1-111111111000000001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-222-200001-1-11-111-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ532222-2-2-2-2-2-22-22-2-1-2-22222-1-1-1-1-1-1-111111111000000001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32-2-220000-111-11-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ542222-2-2-2-2-2-22-22-2-1-2-22222-1-1-1-1-1-1-111111111000000001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-222-200001-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ552222-2-2-2-2-2-2-22-22222-222-2-2-2222-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-22-22222-222-2-2-2222-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ572222-2-2-2-2-2-2-22-22-122-222-211-1-1-111-1-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i00000000−i3i3−i3i3i3−i3i3−i33−33−3−33−330000000000000000
χ582222-2-2-2-2-2-2-22-22-122-222-211-1-1-111-1-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−iii−i−iiiii−i−iii−i−i00000000i3−i3i3−i3−i3i3−i3i3−33−333−33−30000000000000000
χ592222-2-2-2-2-2-2-22-22-122-222-211-1-1-111-1-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii00000000−i3i3−i3i3i3−i3i3−i3−33−333−33−30000000000000000
χ602222-2-2-2-2-2-2-22-22-122-222-211-1-1-111-1-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii00000000i3−i3i3−i3−i3i3−i3i33−33−3−33−330000000000000000
χ612-2-2222-2-22-222-2-222-222-2-2222-2-2-2-222-2-222-2-2000000002-22-22-22-200000000000000000000000000000000000000002-22-2000000000000
χ622-2-2222-2-22-222-2-222-222-2-2222-2-2-2-222-2-222-2-2000000002-22-22-22-20000000000000000000000000000000000000000-22-22000000000000
χ632-2-2222-2-22-2-2-2222-22-22-22-2-22-2-222-2-22222-2-2000000002-2-22-222-2000000000000000000000000000000000000000000002-22-200000000
χ642-2-2222-2-22-2-2-2222-22-22-22-2-22-2-222-2-22222-2-2000000002-2-22-222-200000000000000000000000000000000000000000000-22-2200000000
χ652-2-2222-2-2-222-2-2222-2-2-222222-2-2-2-222-2-222-2-200000000-22-22-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ662-2-2222-2-2-222-2-2222-2-2-222222-2-2-2-222-2-222-2-200000000-22-22-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ672-2-2222-2-2-22-222-22-222-22-2-2-22-2-222-2-22222-2-200000000-222-22-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ682-2-2222-2-2-22-222-22-222-22-2-2-22-2-222-2-22222-2-200000000-222-22-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ692-2-22-2-2222-222-2-22-22-2-222222-2-2-2-2-2-222-2-222000000002-22-2-22-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ702-2-22-2-2222-222-2-22-22-2-222222-2-2-2-2-2-222-2-222000000002-22-2-22-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ712-2-22-2-2222-2-2-22222-22-22-2-2-22-2-22222-2-2-2-222000000002-2-222-2-2200000000000000000000000000000000000000002-2-22000000000000
χ722-2-22-2-2222-2-2-22222-22-22-2-2-22-2-22222-2-2-2-222000000002-2-222-2-220000000000000000000000000000000000000000-222-2000000000000
χ732-2-22-2-222-222-2-222-2222-2-2222-2-2-2-2-2-222-2-22200000000-22-222-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ742-2-22-2-222-222-2-222-2222-2-2222-2-2-2-2-2-222-2-22200000000-22-222-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ752-2-22-2-222-22-222-222-2-22-22-2-22-2-22222-2-2-2-22200000000-222-2-222-20000000000000000000000000000000000000000000000002-2-220000
χ762-2-22-2-222-22-222-222-2-22-22-2-22-2-22222-2-2-2-22200000000-222-2-222-2000000000000000000000000000000000000000000000000-222-20000
χ7744-4-44i−4i4i−4i000000400000000-44-40000004i−4i4i−4i002+2i−2−2i002−2i−2+2i00000000002+2i−2−2i002+2i−2−2i002−2i−2+2i002−2i−2+2i0000000000000000000000000000000000000000
χ7844-4-44i−4i4i−4i000000400000000-44-40000004i−4i4i−4i00−2−2i2+2i00−2+2i2−2i0000000000−2−2i2+2i00−2−2i2+2i00−2+2i2−2i00−2+2i2−2i0000000000000000000000000000000000000000
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χ1084-4-44-4-444-44-444-4-24-4-44-4422-222-2-2-2-22222-2-2000000002-2-222-2-2200000000000000000000000000000000000000000000000000000000

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