Finite Group Databasebeta

← Group #10703030

Character table — Group #10703030

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422222234444446661212121266666612121212121244444444444412121212121212121212121212121212121212121212121244444444224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i-1-111
χ121111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iii-1-111
χ141111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−i11-1-1
χ151111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii11-1-1
χ161111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i-1-111
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-2-22-2-2-222-2222222222-2-2-2-2-2-2-2-22200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ222222222222-2-2-2-22-2-2-222-2222222222-2-2-2-2-2-2-2-2220000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ232222222222-2-2-2-2-1-2-2-222-2-1-1-1-1-1-1-1-1-111111111-1-100002i−2i2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii33−3−333−3−300000000000000000000
χ242222222222-2-2-2-2-1-2-2-222-2-1-1-1-1-1-1-1-1-111111111-1-100002i−2i2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−3−333−3−33300000000000000000000
χ252222222222-2-2-2-2-1-2-2-222-2-1-1-1-1-1-1-1-1-111111111-1-10000−2i2i−2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−33300000000000000000000
χ262222222222-2-2-2-2-1-2-2-222-2-1-1-1-1-1-1-1-1-111111111-1-10000−2i2i−2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i33−3−333−3−300000000000000000000
χ2722222222-2-222-2-222-2-2-2-222222222-2-22-22-222-2-2-2-2000000000000000000000000000000000000000000002-2-2200000000
χ2822222222-2-222-2-222-2-2-2-222222222-2-22-22-222-2-2-2-200000000000000000000000000000000000000000000-222-200000000
χ2922222222-2-2-2-2222-222-2-2-22222222-2-2-22-22-2-222-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ3022222222-2-2-2-2222-222-2-2-22222222-2-2-22-22-2-222-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ312222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200002-2-2200000000000022-2-2-2-2220000000000000000000000000000
χ322222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000-222-2000000000000-2-22222-2-20000000000000000000000000000
χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002-2-220000−i3−i3i3i3i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000000000
χ342222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002-2-220000i3i3−i3−i3−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000000000
χ352222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000-222-20000−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000000000
χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000-222-20000i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000000000
χ372222-2-2-2-222-2-2-2-2-1222-2-22-1-1-11111-1-11111-1-1-1-11122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ382222-2-2-2-222-2-2-2-2-1222-2-22-1-1-11111-1-11111-1-1-1-11122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ392222-2-2-2-222-2-2-2-2-1222-2-22-1-1-11111-1-11111-1-1-1-111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ402222-2-2-2-222-2-2-2-2-1222-2-22-1-1-11111-1-11111-1-1-1-111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ412222-2-2-2-2-2-222-2-22-22222-2222-2-2-2-2-2-22-22-2-2-222220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ422222-2-2-2-2-2-222-2-22-22222-2222-2-2-2-2-2-22-22-2-2-22222000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ432222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-22-2222-2-2220000000000000000000000000000000000000000000022-2-200000000
χ442222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-22-2222-2-22200000000000000000000000000000000000000000000-2-22200000000
χ452-2-2222-2-22-22-22-22-22-22-222-2-222-2-22-22-2-222-22-22-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-2-2222-2-22-22-22-22-22-22-222-2-222-2-22-22-2-222-22-22-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-2-2222-2-22-22-22-2-1-22-22-22-111-1-111-11-111-1-11-11-11000000002i−2i2i−2i3−33−33−33−3−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii00000000000000000000
χ482-2-2222-2-22-22-22-2-1-22-22-22-111-1-111-11-111-1-11-11-11000000002i−2i2i−2i−33−33−33−33i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii00000000000000000000
χ492-2-2222-2-22-22-22-2-1-22-22-22-111-1-111-11-111-1-11-11-1100000000−2i2i−2i2i3−33−33−33−3i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i00000000000000000000
χ502-2-2222-2-22-22-22-2-1-22-22-22-111-1-111-11-111-1-11-11-1100000000−2i2i−2i2i−33−33−33−33−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i00000000000000000000
χ512-2-2222-2-22-2-22-2222-222-2-22-2-222-2-22-2-222-2-22-222-22i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ522-2-2222-2-22-2-22-2222-222-2-22-2-222-2-22-2-222-2-22-222-2−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ532-2-2222-2-22-2-22-22-12-222-2-2-111-1-111-111-1-111-11-1-112i−2i2i−2i00000000−iii−i−iii−i3−3−333−3−33i3−i3−i3i3i3−i3−i3i300000000000000000000
χ542-2-2222-2-22-2-22-22-12-222-2-2-111-1-111-111-1-111-11-1-112i−2i2i−2i00000000−iii−i−iii−i−333−3−333−3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ552-2-2222-2-22-2-22-22-12-222-2-2-111-1-111-111-1-111-11-1-11−2i2i−2i2i00000000i−i−iii−i−ii3−3−333−3−33−i3i3i3−i3−i3i3i3−i300000000000000000000
χ562-2-2222-2-22-2-22-22-12-222-2-2-111-1-111-111-1-111-11-1-11−2i2i−2i2i00000000i−i−iii−i−ii−333−3−333−3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ572-2-2222-2-2-222-2-222-2-22-2222-2-222-2-2-2222-2-22-2-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ582-2-2222-2-2-222-2-222-2-22-2222-2-222-2-2-2222-2-22-2-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ592-2-2222-2-2-22-222-2222-2-22-22-2-222-2-2-22-2-222-222-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ602-2-2222-2-2-22-222-2222-2-22-22-2-222-2-2-22-2-222-222-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ612-2-22-2-2222-22-22-222-22-22-22-2-2-2-2222-22-2-22-22-22-222i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ622-2-22-2-2222-22-22-222-22-22-22-2-2-2-2222-22-2-22-22-22-22−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ632-2-22-2-2222-22-22-2-12-22-22-2-11111-1-1-11-111-11-11-11-12i−2i−2i2i00000000−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i33−3−33−333−300000000000000000000
χ642-2-22-2-2222-22-22-2-12-22-22-2-11111-1-1-11-111-11-11-11-12i−2i−2i2i00000000−iii−ii−i−iii3−i3−i3i3−i3i3i3−i3−333−33−3−3300000000000000000000
χ652-2-22-2-2222-22-22-2-12-22-22-2-11111-1-1-11-111-11-11-11-1−2i2i2i−2i00000000i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i3−333−33−3−3300000000000000000000
χ662-2-22-2-2222-22-22-2-12-22-22-2-11111-1-1-11-111-11-11-11-1−2i2i2i−2i00000000i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i33−3−33−333−300000000000000000000
χ672-2-22-2-2222-2-22-222-22-2-2222-2-2-2-2222-2-222-22-22-2-22000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ682-2-22-2-2222-2-22-222-22-2-2222-2-2-2-2222-2-222-22-22-2-2200000000-222-20000000000000000-22-222-22-200000000000000000000
χ692-2-22-2-2222-2-22-22-1-22-2-222-11111-1-1-111-1-11-11-111-1000000002-2-223−33−3−33−33−33−333−33−3-11-111-11-100000000000000000000
χ702-2-22-2-2222-2-22-22-1-22-2-222-11111-1-1-111-1-11-11-111-1000000002-2-22−33−333−33−33−33−3−33−33-11-111-11-100000000000000000000
χ712-2-22-2-2222-2-22-22-1-22-2-222-11111-1-1-111-1-11-11-111-100000000-222-23−33−3−33−333−33−3−33−331-11-1-11-1100000000000000000000
χ722-2-22-2-2222-2-22-22-1-22-2-222-11111-1-1-111-1-11-11-111-100000000-222-2−33−333−33−3−33−333−33−31-11-1-11-1100000000000000000000
χ732-2-22-2-222-222-2-22222-22-2-22-2-2-2-222-2222-2-2-222-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ742-2-22-2-222-222-2-22222-22-2-22-2-2-2-222-2222-2-2-222-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ752-2-22-2-222-22-222-22-2-222-222-2-2-2-222-22-2-2222-2-222-20000000000000000000000000000000000000000000000002-2-220000
χ762-2-22-2-222-22-222-22-2-222-222-2-2-2-222-22-2-2222-2-222-2000000000000000000000000000000000000000000000000-222-20000
χ7744444444-4-444-4-4-24-4-4-4-44-2-2-2-2-2-2-222-22-22-2-2222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-444-2-444-4-4-4-2-2-2-2-2-2-2222-22-222-2-22200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-4-444-4-4-2-44444-4-2-2-2222222-22-2222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-4-4-444-24-4-4444-2-2-22222222-22-2-2-222-2-200000000000000000000000000000000000000000000000000000000
χ8144-4-44i−4i4i−4i0000004000000-44-44i−4i4i−4i000000000000000000000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000
χ8244-4-44i−4i4i−4i0000004000000-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000
χ8344-4-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000
χ8444-4-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000
χ854-44-44i−4i−4i4i0000004000000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002+2i−2−2i002−2i−2+2i00000000000000
χ864-44-44i−4i−4i4i0000004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i00000000000000
χ874-44-4−4i4i4i−4i0000004000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002−2i−2+2i002+2i−2−2i00000000000000
χ884-44-4−4i4i4i−4i0000004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i00000000000000
χ894-4-4444-4-4-444-4-44-2-4-44-444-222-2-2222-2-2-222-222-22-200000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-44-444-4-244-4-44-4-222-2-2222-222-2-22-2-222-200000000000000000000000000000000000000000000000000000000
χ914-4-44-4-444-444-4-44-244-44-4-4-22222-2-22-2-2-2222-2-22-2200000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-444-4-2-4-444-44-22222-2-22-222-2-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000000-40000004-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8−8i8i−8i8i000000-40000004-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88i−8i−8i8i000000-400000044-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i000000-400000044-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).