Finite Group Databasebeta

← Group #10823690

Character table — Group #10823690

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121222224444666666666666121212121212121212121212244444446612121212121212121212121212122244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11-111-1-11-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-11-1-111-111111-1-1-1-1
χ91111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-11-11-11-1-1111-1-111-1-1
χ101111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-11-11-111-1-1-111-1-111
χ111111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111111-1-11-1-111-1-1-1-111
χ121111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1-111-111-1-11111-1-1
χ131111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-11-11-11-1-11-1-111-1-111
χ141111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-11-11-111-111-1-111-1-1
χ151111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-1
χ161111-1-1-1-11111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11111-1-1-1-111
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
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-111111111-1-10000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-2-2-22222111111-1-1-1-1-1-1-1-1110000000000000000
χ212222222222-2-2-2-2222-2-2-2-222222222222222200000000-2-2-2-200000000-2-2-2-2000000002-2-22000022-2-2-2-200000000220000000000000000
χ222222222222-2-2-2-2222-2-2-2-222222222222222200000000-2-2-2-200000000-2-2-2-200000000-222-20000-2-2222200000000-2-20000000000000000
χ232222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111−i3−i3−i3−i3i3i3i3i31111−i3−i3−i3−i3i3i3i3i32-2-220000-1-11111−i3−i3i3i3−i3−i3i3i3-1-10000000000000000
χ242222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111−i3−i3−i3−i3i3i3i3i31111−i3−i3−i3−i3i3i3i3i3-222-2000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3110000000000000000
χ252222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111i3i3i3i3−i3−i3−i3−i31111i3i3i3i3−i3−i3−i3−i32-2-220000-1-11111i3i3−i3−i3i3i3−i3−i3-1-10000000000000000
χ262222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000001111i3i3i3i3−i3−i3−i3−i31111i3i3i3i3−i3−i3−i3−i3-222-2000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3110000000000000000
χ2722222222-2-222-2-22-2-222-2-222-2-2-2-222222-2-2-2-20000000022-2-20000000022-2-2000000000000000000000000000000000200-2-20200000000
χ2822222222-2-222-2-22-2-222-2-222-2-2-2-222222-2-2-2-20000000022-2-20000000022-2-2000000000000000000000000000000000-200220-200000000
χ2922222222-2-2-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-200000000-2-22200000000-2-2220000000000000000000000000000000020-2-2002000000000
χ3022222222-2-2-2-2222-2-2-2-22222-2-2-2-222222-2-2-2-200000000-2-22200000000-2-22200000000000000000000000000000000-202200-2000000000
χ312222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-222-2-2-1-1-1-111-1-1-1-11111110000000000000000
χ322222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111-2-222-2-2221111-1-11111-1-1-1-1-1-10000000000000000
χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1111111-1-1-1-1110000000000000000
χ342222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-11111-1-10000000000000000
χ352222-2-2-2-222-2-2-2-22-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000002222000000002-22-2000022-2-22200000000-2-20000000000000000
χ362222-2-2-2-222-2-2-2-22-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-200000000222200000000-22-220000-2-222-2-200000000220000000000000000
χ372222-2-2-2-222-2-2-2-2-1-2-22222-1-1-1-1-1-1-111111111000000001111−i3−i3−i3−i3i3i3i3i3-1-1-1-1i3i3i3i3−i3−i3−i3−i32-22-20000-1-111-1-1−i3−i3i3i3i3i3−i3−i3110000000000000000
χ382222-2-2-2-222-2-2-2-2-1-2-22222-1-1-1-1-1-1-111111111000000001111−i3−i3−i3−i3i3i3i3i3-1-1-1-1i3i3i3i3−i3−i3−i3−i3-22-22000011-1-111i3i3−i3−i3−i3−i3i3i3-1-10000000000000000
χ392222-2-2-2-222-2-2-2-2-1-2-22222-1-1-1-1-1-1-111111111000000001111i3i3i3i3−i3−i3−i3−i3-1-1-1-1−i3−i3−i3−i3i3i3i3i32-22-20000-1-111-1-1i3i3−i3−i3−i3−i3i3i3110000000000000000
χ402222-2-2-2-222-2-2-2-2-1-2-22222-1-1-1-1-1-1-111111111000000001111i3i3i3i3−i3−i3−i3−i3-1-1-1-1−i3−i3−i3−i3i3i3i3i3-22-22000011-1-111−i3−i3i3i3i3i3−i3−i3-1-10000000000000000
χ412222-2-2-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-222220000000022-2-200000000-2-2220000000000000000000000000000000002002-20-200000000
χ422222-2-2-2-2-2-222-2-2222-2-22222-2-2-2-22-2-2-2-222220000000022-2-200000000-2-222000000000000000000000000000000000-200-220200000000
χ432222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-22-2-2-2-2222200000000-2-2220000000022-2-20000000000000000000000000000000020-2200-2000000000
χ442222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-22-2-2-2-2222200000000-2-2220000000022-2-200000000000000000000000000000000-202-2002000000000
χ4522-2-22i2i−2i−2i2-22-22-222i−2i2i−2i2i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-22-2000000002i−2i2i−2i000000000000000000000000000000000000000000002i−2i2-2
χ4622-2-22i2i−2i−2i2-22-22-222i−2i2i−2i2i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-22-2000000002i−2i2i−2i00000000000000000000000000000000000000000000−2i2i-22
χ4722-2-22i2i−2i−2i2-2-22-2222i−2i−2i2i−2i2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000-22-2200000000−2i2i−2i2i00000000000000000000000000000000000000002-22i−2i0000
χ4822-2-22i2i−2i−2i2-2-22-2222i−2i−2i2i−2i2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000-22-2200000000−2i2i−2i2i0000000000000000000000000000000000000000-22−2i2i0000
χ4922-2-22i2i−2i−2i-222-2-222−2i2i2i−2i−2i2i2-2-2-222-22i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i2-2-2222-2-222-2-22i−2i−2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5022-2-22i2i−2i−2i-222-2-222−2i2i2i−2i−2i2i2-2-2-222-22i2i−2i−2i−2i−2i2i2i-2-222−2i−2i2i2i2-2-22-2-222-2-2222i−2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5122-2-22i2i−2i−2i-222-2-22-1−2i2i2i−2i−2i2i-1111-1-11−i−iiiii−i−i22-2-22i2i−2i−2i-111-1-1-111-1-111−iii−i−i−iii−i−iii00000000−i3i3−i3i33−3−i3i3−i3i33−33−33−30000000000000000
χ5222-2-22i2i−2i−2i-222-2-22-1−2i2i2i−2i−2i2i-1111-1-11−i−iiiii−i−i22-2-22i2i−2i−2i-111-1-1-111-1-111−iii−i−i−iii−i−iii00000000i3−i3i3−i3−33i3−i3i3−i3−33−33−330000000000000000
χ5322-2-22i2i−2i−2i-222-2-22-1−2i2i2i−2i−2i2i-1111-1-11−i−iiiii−i−i-2-222−2i−2i2i2i-111-111-1-111-1-1−iii−iii−i−iii−i−i00000000−i3i3−i3i33−3i3−i3i3−i3−33−333−30000000000000000
χ5422-2-22i2i−2i−2i-222-2-22-1−2i2i2i−2i−2i2i-1111-1-11−i−iiiii−i−i-2-222−2i−2i2i2i-111-111-1-111-1-1−iii−iii−i−iii−i−i00000000i3−i3i3−i3−33−i3i3−i3i33−33−3−330000000000000000
χ5522-2-22i2i−2i−2i-22-222-22−2i2i−2i2i2i−2i2-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000-222-200000000−2i2i2i−2i0000000000002-22i−2i0000002-2-222i−2i−2i2i000000000000000000
χ5622-2-22i2i−2i−2i-22-222-22−2i2i−2i2i2i−2i2-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000-222-200000000−2i2i2i−2i000000000000-22−2i2i000000-222-2−2i2i2i−2i000000000000000000
χ5722-2-22i2i−2i−2i-22-222-2-1−2i2i−2i2i2i−2i-1111-1-11−i−iiiii−i−i000000001-1-11−i3−i3i3i3i3i3−i3−i3i−i−ii33−3−3−3−33300002-22i−2i−i3i3i3−i3−33-111-1−iii−i3−30000000000000000
χ5822-2-22i2i−2i−2i-22-222-2-1−2i2i−2i2i2i−2i-1111-1-11−i−iiiii−i−i000000001-1-11−i3−i3i3i3i3i3−i3−i3i−i−ii33−3−3−3−3330000-22−2i2ii3−i3−i3i33−31-1-11i−i−ii−330000000000000000
χ5922-2-22i2i−2i−2i-22-222-2-1−2i2i−2i2i2i−2i-1111-1-11−i−iiiii−i−i000000001-1-11i3i3−i3−i3−i3−i3i3i3i−i−ii−3−33333−3−300002-22i−2ii3−i3−i3i33−3-111-1−iii−i−330000000000000000
χ6022-2-22i2i−2i−2i-22-222-2-1−2i2i−2i2i2i−2i-1111-1-11−i−iiiii−i−i000000001-1-11i3i3−i3−i3−i3−i3i3i3i−i−ii−3−33333−3−30000-22−2i2i−i3i3i3−i3−331-1-11i−i−ii3−30000000000000000
χ6122-2-2−2i−2i2i2i2-22-22-22−2i2i−2i2i−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-22-200000000−2i2i−2i2i000000000000000000000000000000000000000000002i−2i-22
χ6222-2-2−2i−2i2i2i2-22-22-22−2i2i−2i2i−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-22-200000000−2i2i−2i2i00000000000000000000000000000000000000000000−2i2i2-2
χ6322-2-2−2i−2i2i2i2-2-22-222−2i2i2i−2i2i−2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-22-22000000002i−2i2i−2i00000000000000000000000000000000000000002-2−2i2i0000
χ6422-2-2−2i−2i2i2i2-2-22-222−2i2i2i−2i2i−2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-22-22000000002i−2i2i−2i0000000000000000000000000000000000000000-222i−2i0000
χ6522-2-2−2i−2i2i2i-222-2-2222i−2i−2i2i2i−2i2-2-2-222-2−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i2-2-2222-2-222-2-2−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6622-2-2−2i−2i2i2i-222-2-2222i−2i−2i2i2i−2i2-2-2-222-2−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i2-2-22-2-222-2-222−2i2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ6722-2-2−2i−2i2i2i-222-2-22-12i−2i−2i2i2i−2i-1111-1-11ii−i−i−i−iii22-2-2−2i−2i2i2i-111-1-1-111-1-111i−i−iiii−i−iii−i−i00000000−i3i3−i3i3−33−i3i3−i3i3−33−33−330000000000000000
χ6822-2-2−2i−2i2i2i-222-2-22-12i−2i−2i2i2i−2i-1111-1-11ii−i−i−i−iii22-2-2−2i−2i2i2i-111-1-1-111-1-111i−i−iiii−i−iii−i−i00000000i3−i3i3−i33−3i3−i3i3−i33−33−33−30000000000000000
χ6922-2-2−2i−2i2i2i-222-2-22-12i−2i−2i2i2i−2i-1111-1-11ii−i−i−i−iii-2-2222i2i−2i−2i-111-111-1-111-1-1i−i−ii−i−iii−i−iii00000000−i3i3−i3i3−33i3−i3i3−i33−33−3−330000000000000000
χ7022-2-2−2i−2i2i2i-222-2-22-12i−2i−2i2i2i−2i-1111-1-11ii−i−i−i−iii-2-2222i2i−2i−2i-111-111-1-111-1-1i−i−ii−i−iii−i−iii00000000i3−i3i3−i33−3−i3i3−i3i3−33−333−30000000000000000
χ7122-2-2−2i−2i2i2i-22-222-222i−2i2i−2i−2i2i2-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000-222-2000000002i−2i−2i2i0000000000002-2−2i2i0000002-2-22−2i2i2i−2i000000000000000000
χ7222-2-2−2i−2i2i2i-22-222-222i−2i2i−2i−2i2i2-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000-222-2000000002i−2i−2i2i000000000000-222i−2i000000-222-22i−2i−2i2i000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.