Finite Group Databasebeta

← Group #10702899

Character table — Group #10702899

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
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ9111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ10111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii
χ11111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ12111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−i
χ13111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ14111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11ii−i−i−i−iii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ15111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ16111-1-1-1-1111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11−i−iiiii−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
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
χ212222222222-2-2-22-2-2-2-22-22222222222-2-2-2-222-2-2-2-2000000002-22-2000000000000000022-2-222-2-200000000000000000000
χ222222222222-2-2-22-2-2-2-22-22222222222-2-2-2-222-2-2-2-200000000-22-220000000000000000-2-222-2-22200000000000000000000
χ232222222222-2-2-22-2-2-2-22-2-1-1-1-1-1-1-1-1-1-11111-1-11111000000002-22-2−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000000000
χ242222222222-2-2-22-2-2-2-22-2-1-1-1-1-1-1-1-1-1-11111-1-11111000000002-22-2i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000000000
χ252222222222-2-2-22-2-2-2-22-2-1-1-1-1-1-1-1-1-1-11111-1-1111100000000-22-22−i3i3−i3i3−i3i3−i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000000000
χ262222222222-2-2-22-2-2-2-22-2-1-1-1-1-1-1-1-1-1-11111-1-1111100000000-22-22i3−i3i3−i3i3−i3i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000000000
χ2722222222-2-222-2-22-2-2-2-2222222222-2-222-2-2-2-222-2-200002-22-20000000000002-22-22-22-20000000000000000000000000000
χ2822222222-2-222-2-22-2-2-2-2222222222-2-222-2-2-2-222-2-20000-22-22000000000000-22-22-22-220000000000000000000000000000
χ2922222222-2-222-2-22-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-1-11100002-22-20000−i3i3−i3i3i3−i3i3−i3-11-11-11-11−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3022222222-2-222-2-22-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-1-11100002-22-20000i3−i3i3−i3−i3i3−i3i3-11-11-11-11i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3122222222-2-222-2-22-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-1-1110000-22-220000−i3i3−i3i3i3−i3i3−i31-11-11-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3222222222-2-222-2-22-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-1-1110000-22-220000i3−i3i3−i3−i3i3−i3i31-11-11-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3322222222-2-2-2-22-2-2222-2-222222222-2-2-2-222-2-2-2-22222-2-2000000002222-2-2-2-2000000000000000000000000000000000000
χ3422222222-2-2-2-22-2-2222-2-222222222-2-2-2-222-2-2-2-222-2-22200000000-2-2-2-22222000000000000000000000000000000000000
χ3522222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-11111-1-11111-1-122-2-200000000-1-1-1-11111−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ3622222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-11111-1-11111-1-122-2-200000000-1-1-1-11111i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3722222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-11111-1-11111-1-1-2-222000000001111-1-1-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3822222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-11111-1-11111-1-1-2-222000000001111-1-1-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ39222-2-2-2-2222222-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111112-22-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ40222-2-2-2-2222222-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-11111112-22-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ41222-2-2-2-2222222-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-1111111-22-222i2i−2i−2i−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ42222-2-2-2-2222222-2-2-2-22-2-2-1-1-1-11111-1-1-1-1-1-1111111-22-22−2i−2i2i2i2i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ43222-2-2-2-2222-2-2-2-2222-2-222222-2-2-2-222-2-2-2-2-2-22222000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ44222-2-2-2-2222-2-2-2-2222-2-222222-2-2-2-222-2-2-2-2-2-2222200000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ45222-2-2-2-2222-2-2-2-2222-2-22-1-1-1-11111-1-1111111-1-1-1-1000000002i−2i−2i2i−i3i3i3−i3−i3i3i3−i333−3−3−3−333−i−iiiii−i−i00000000000000000000
χ46222-2-2-2-2222-2-2-2-2222-2-22-1-1-1-11111-1-1111111-1-1-1-1000000002i−2i−2i2ii3−i3−i3i3i3−i3−i3i3−3−33333−3−3−i−iiiii−i−i00000000000000000000
χ47222-2-2-2-2222-2-2-2-2222-2-22-1-1-1-11111-1-1111111-1-1-1-100000000−2i2i2i−2i−i3i3i3−i3−i3i3i3−i3−3−33333−3−3ii−i−i−i−iii00000000000000000000
χ48222-2-2-2-2222-2-2-2-2222-2-22-1-1-1-11111-1-1111111-1-1-1-100000000−2i2i2i−2ii3−i3−i3i3i3−i3−i3i333−3−3−3−333ii−i−i−i−iii00000000000000000000
χ49222-2-2-2-22-2-222-22-222-22-22222-2-2-2-2-2-222-2-222-2-22200002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ50222-2-2-2-22-2-222-22-222-22-22222-2-2-2-2-2-222-2-222-2-2220000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ51222-2-2-2-22-2-222-22-222-22-2-1-1-1-1111111-1-111-1-111-1-100002i−2i−2i2i0000−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i3−33−3−33−3300000000000000000000
χ52222-2-2-2-22-2-222-22-222-22-2-1-1-1-1111111-1-111-1-111-1-100002i−2i−2i2i0000i3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i−33−333−33−300000000000000000000
χ53222-2-2-2-22-2-222-22-222-22-2-1-1-1-1111111-1-111-1-111-1-10000−2i2i2i−2i0000−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii−33−333−33−300000000000000000000
χ54222-2-2-2-22-2-222-22-222-22-2-1-1-1-1111111-1-111-1-111-1-10000−2i2i2i−2i0000i3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii3−33−3−33−3300000000000000000000
χ55222-2-2-2-22-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2222222-2-22-2-220000000022-2-2-2-222000000000000000000000000000000000000
χ56222-2-2-2-22-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2222222-2-2-222-200000000-2-22222-2-2000000000000000000000000000000000000
χ57222-2-2-2-22-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1-1-1112-2-2200000000-1-11111-1-13−3−33−333−33−3−33−333−300000000000000000000
χ58222-2-2-2-22-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1-1-1112-2-2200000000-1-11111-1-1−333−33−3−33−333−33−3−3300000000000000000000
χ59222-2-2-2-22-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1-1-111-222-20000000011-1-1-1-1113−3−33−333−3−333−33−3−3300000000000000000000
χ60222-2-2-2-22-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1-1-111-222-20000000011-1-1-1-111−333−33−3−333−3−33−333−300000000000000000000
χ612-2222-2-2-22-22-222-22-2-2-222-2-2222-2-22-22-22-22-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ622-2222-2-2-22-22-222-22-2-2-222-2-2222-2-22-22-22-22-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ632-2222-2-2-22-2-22-222-222-2-22-2-2222-2-22-2-22-222-2-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ642-2222-2-2-22-2-22-222-222-2-22-2-2222-2-22-2-22-222-2-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ652-2222-2-2-2-222-2-2-2-2-222222-2-2222-2-2-222-2-22-222-2-2200000000000000000000000000000000000000000000000000002-22-2
χ662-2222-2-2-2-222-2-2-2-2-222222-2-2222-2-2-222-2-22-222-2-220000000000000000000000000000000000000000000000000000-22-22
χ672-2222-2-2-2-22-222-222-2-22-22-2-2222-2-2-22-222-2-22-222-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ682-2222-2-2-2-22-222-222-2-22-22-2-2222-2-2-22-222-2-22-222-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ692-22-2-222-22-22-22-22-22-22-22-2-22-2-2222-22-22-2-22-22-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ702-22-2-222-22-22-22-22-22-22-22-2-22-2-2222-22-22-2-22-22-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ712-22-2-222-22-2-22-2-2-22-22222-2-22-2-2222-2-22-22-222-22-20000000000000000000000000000000000000000000000002-2-220000
χ722-22-2-222-22-2-22-2-2-22-22222-2-22-2-2222-2-22-22-222-22-2000000000000000000000000000000000000000000000000-222-20000
χ732-22-2-222-2-222-2-2222-22-2-22-2-22-2-222-222-2-222-2-222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ742-22-2-222-2-222-2-2222-22-2-22-2-22-2-222-222-2-222-2-222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ752-22-2-222-2-22-2222-2-22-2-222-2-22-2-222-22-222-22-22-2-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ762-22-2-222-2-22-2222-2-22-2-222-2-22-2-222-22-222-22-22-2-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ7744-44-44-4-400000000000044-4-44-44-40000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ7844-44-44-4-400000000000044-4-44-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ7944-4-44-44-400000000000044-4-4-44-440000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ8044-4-44-44-400000000000044-4-4-44-44000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ814-4444-4-4-44-44-444-44-4-4-44-222-2-2-222-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ824-4444-4-4-44-4-44-444-444-4-4-222-2-2-222-222-22-2-222-22-200000000000000000000000000000000000000000000000000000000
χ834-4444-4-4-4-444-4-4-4-4-44444-222-2-2-2222-2-222-22-2-222-200000000000000000000000000000000000000000000000000000000
χ844-4444-4-4-4-44-444-444-4-44-4-222-2-2-2222-22-2-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ854-44-4-444-44-44-44-44-44-44-4-222-222-2-2-22-22-222-22-22-200000000000000000000000000000000000000000000000000000000
χ864-44-4-444-44-4-44-4-4-44-4444-222-222-2-2-222-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ874-44-4-444-4-444-4-4444-44-4-4-222-222-2-22-2-222-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ884-44-4-444-4-44-4444-4-44-4-44-222-222-2-22-22-2-22-22-222-200000000000000000000000000000000000000000000000000000000
χ894-4-44-4-4440000000000004-44-44-4-440000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ904-4-44-4-4440000000000004-44-44-4-44000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ914-4-4-444-440000000000004-44-4-444-40000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ924-4-4-444-440000000000004-44-4-444-4000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ9388-88-88-8-8000000000000-4-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-88-8000000000000-4-4444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-8-888000000000000-44-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88000000000000-44-444-4-4400000000000000000000000000000000000000000000000000000000000000000000

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