Finite Group Databasebeta

← Group #10702895

Character table — Group #10702895

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222222222222366666666666666666662244444444446666121212121212121212121212121212121212121244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1
χ10111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111
χ11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1
χ12111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111
χ13111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii-1-111
χ14111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i11-1-1
χ15111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i-1-111
χ16111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii11-1-1
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-22-2-2-22-2-22222222222-2-2-2-22-2-2-22-2000000000000000000000000000000000000000000002-22-200000000
χ222222222222-2-2-22-2-2-22-2-22222222222-2-2-2-22-2-2-22-200000000000000000000000000000000000000000000-22-2200000000
χ2322222222-2-222-2-22-2-2-22-222222222-2-222-2-2-22-2-2-220000000000000000000000000000000000000000000000002-22-20000
χ2422222222-2-222-2-22-2-2-22-222222222-2-222-2-2-22-2-2-22000000000000000000000000000000000000000000000000-22-220000
χ2522222222-2-2-2-22-2-222-2-2222222222-2-2-2-222-2-222-2-222-2-2000000002222-2-2-2-2000000000000000000000000000000000000
χ2622222222-2-2-2-22-2-222-2-2222222222-2-2-2-222-2-222-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000
χ2722222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-11122-2-200000000-1-1-1-1111133−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-11122-2-200000000-1-1-1-11111−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-111-2-222000000001111-1-1-1-133−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-111-2-222000000001111-1-1-1-1−3−333−3−33333−3−333−3−300000000000000000000
χ31222-2-2-2-2222222-2-2-2-2-2-22-1-1-11111-1-1-1-1-1-1-11111112-22-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ32222-2-2-2-2222222-2-2-2-2-2-22-1-1-11111-1-1-1-1-1-1-11111112-22-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ33222-2-2-2-2222222-2-2-2-2-2-22-1-1-11111-1-1-1-1-1-1-1111111-22-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ34222-2-2-2-2222222-2-2-2-2-2-22-1-1-11111-1-1-1-1-1-1-1111111-22-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ35222-2-2-2-2222-2-2-2-2222-22-2222-2-2-2-2222-2-2-2-2-2222-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ36222-2-2-2-2222-2-2-2-2222-22-2222-2-2-2-2222-2-2-2-2-2222-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ37222-2-2-2-22-2-222-22-2222-2-2222-2-2-2-22-2-222-2-22-2222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ38222-2-2-2-22-2-222-22-2222-2-2222-2-2-2-22-2-222-2-22-2222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ39222-2-2-2-22-2-2-2-2222-2-2222222-2-2-2-22-2-2-2-22222-2-2222-2-220000000022-2-2-2-222000000000000000000000000000000000000
χ40222-2-2-2-22-2-2-2-2222-2-2222222-2-2-2-22-2-2-2-22222-2-222-222-200000000-2-22222-2-2000000000000000000000000000000000000
χ41222-2-2-2-22-2-2-2-2222-2-2222-1-1-11111-11111-1-1-1-111-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ42222-2-2-2-22-2-2-2-2222-2-2222-1-1-11111-11111-1-1-1-111-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ43222-2-2-2-22-2-2-2-2222-2-2222-1-1-11111-11111-1-1-1-111-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ44222-2-2-2-22-2-2-2-2222-2-2222-1-1-11111-11111-1-1-1-111-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-2222-2-2-22-22-222-22-2-22-22-2-222-2-222-22-22-22-22-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2222-2-2-22-22-222-22-2-22-22-2-222-2-222-22-22-22-22-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2222-2-2-22-2-22-222-22-2-222-2-222-2-222-2-22-2222-22-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ482-2222-2-2-22-2-22-222-22-2-222-2-222-2-222-2-22-2222-22-2-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ492-2222-2-2-22-2-22-222-22-2-22-111-1-111-1-111-11-1-1-11-111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii00000000000000000000
χ502-2222-2-2-22-2-22-222-22-2-22-111-1-111-1-111-11-1-1-11-111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−33−33−33−33−ii−ii−ii−ii00000000000000000000
χ512-2222-2-2-22-2-22-222-22-2-22-111-1-111-1-111-11-1-1-11-11100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i00000000000000000000
χ522-2222-2-2-22-2-22-222-22-2-22-111-1-111-1-111-11-1-1-11-11100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i33−33−33−33−3i−ii−ii−ii−i00000000000000000000
χ532-2222-2-2-2-222-2-2-2-2-222222-2-222-2-22-222-2-22-2-2-222200002-22-20000000000002-2-222-2-220000000000000000000000000000
χ542-2222-2-2-2-222-2-2-2-2-222222-2-222-2-22-222-2-22-2-2-22220000-22-22000000000000-222-2-222-20000000000000000000000000000
χ552-2222-2-2-2-222-2-2-2-2-22222-111-1-111-11-1-111-1111-1-1-100002-22-20000−i3i3−i3i3i3−i3i3−i3-111-1-111-1−i3i3i3−i3−i3i3i3−i300000000000000000000
χ562-2222-2-2-2-222-2-2-2-2-22222-111-1-111-11-1-111-1111-1-1-100002-22-20000i3−i3i3−i3−i3i3−i3i3-111-1-111-1i3−i3−i3i3i3−i3−i3i300000000000000000000
χ572-2222-2-2-2-222-2-2-2-2-22222-111-1-111-11-1-111-1111-1-1-10000-22-220000−i3i3−i3i3i3−i3i3−i31-1-111-1-11i3−i3−i3i3i3−i3−i3i300000000000000000000
χ582-2222-2-2-2-222-2-2-2-2-22222-111-1-111-11-1-111-1111-1-1-10000-22-220000i3−i3i3−i3−i3i3−i3i31-1-111-1-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ592-2222-2-2-2-22-222-222-22-2-22-2-222-2-22-22-222-2-222-22-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ602-2222-2-2-2-22-222-222-22-2-22-2-222-2-22-22-222-2-222-22-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ612-22-2-222-22-22-22-22-222-2-22-2-2-2-22222-22-22-2-22-222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ622-22-2-222-22-22-22-22-222-2-22-2-2-2-22222-22-22-2-22-222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ632-22-2-222-22-2-22-2-2-22-22222-2-2-2-22222-2-22-22-2-22-222000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ642-22-2-222-22-2-22-2-2-22-22222-2-2-2-22222-2-22-22-2-22-22200000000-222-20000000000000000-22-222-22-200000000000000000000
χ652-22-2-222-22-2-22-2-2-22-2222-11111-1-1-1-111-11-111-11-1-1000000002-2-22−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3-11-111-11-100000000000000000000
χ662-22-2-222-22-2-22-2-2-22-2222-11111-1-1-1-111-11-111-11-1-1000000002-2-22i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3-11-111-11-100000000000000000000
χ672-22-2-222-22-2-22-2-2-22-2222-11111-1-1-1-111-11-111-11-1-100000000-222-2−i3i3i3−i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i31-11-1-11-1100000000000000000000
χ682-22-2-222-22-2-22-2-2-22-2222-11111-1-1-1-111-11-111-11-1-100000000-222-2i3−i3−i3i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i31-11-1-11-1100000000000000000000
χ692-22-2-222-2-222-2-2222-2-2-222-2-2-2-2222-222-2-22222-2-2-200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ702-22-2-222-2-222-2-2222-2-2-222-2-2-2-2222-222-2-22222-2-2-20000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ712-22-2-222-2-222-2-2222-2-2-22-11111-1-1-11-1-111-1-1-1-111100002i−2i−2i2i0000−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii3−3−33−333−300000000000000000000
χ722-22-2-222-2-222-2-2222-2-2-22-11111-1-1-11-1-111-1-1-1-111100002i−2i−2i2i0000i3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii−333−33−3−3300000000000000000000
χ732-22-2-222-2-222-2-2222-2-2-22-11111-1-1-11-1-111-1-1-1-11110000−2i2i2i−2i0000−i3i3i3−i3i3−i3−i3i3i−i−ii−iii−i−333−33−3−3300000000000000000000
χ742-22-2-222-2-222-2-2222-2-2-22-11111-1-1-11-1-111-1-1-1-11110000−2i2i2i−2i0000i3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i3−3−33−333−300000000000000000000
χ752-22-2-222-2-22-2222-2-22-22-22-2-2-2-2222-22-222-22-2-22-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ762-22-2-222-2-22-2222-2-22-22-22-2-2-2-2222-22-222-22-2-22-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ774444444444-4-4-44-4-4-44-4-4-2-2-2-2-2-2-2-2-2-22222-2222-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-444-4-44-4-4-44-4-2-2-2-2-2-2-2-222-2-2222-2222-200000000000000000000000000000000000000000000000000000000
χ79444-4-4-4-4444-4-4-4-4444-44-4-2-2-22222-2-2-222222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ80444-4-4-4-44-4-444-44-4444-4-4-2-2-22222-222-2-222-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-400000000000044-44-44-4-40000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ8244-44-44-4-400000000000044-44-44-4-4000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ8344-4-44-44-400000000000044-4-44-44-40000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ8444-4-44-44-400000000000044-4-44-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ854-4444-4-4-44-44-444-44-4-44-4-222-2-222-2-22-22-22-22-222-200000000000000000000000000000000000000000000000000000000
χ864-4444-4-4-4-44-444-444-44-4-4-222-2-222-22-22-2-222-2-22-2200000000000000000000000000000000000000000000000000000000
χ874-44-4-444-44-44-44-44-444-4-4-22222-2-2-2-22-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ884-44-4-444-4-44-4444-4-44-44-4-22222-2-2-22-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ894-4-44-4-4440000000000004-444-4-44-40000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ904-4-44-4-4440000000000004-444-4-44-4000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ914-4-4-444-440000000000004-44-444-4-40000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ924-4-4-444-440000000000004-44-444-4-4000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ9388-88-88-8-8000000000000-4-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-88-8000000000000-4-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-8-888000000000000-44-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88000000000000-44-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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