Finite Group Databasebeta

← Group #10702678

Character table — Group #10702678

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222234444444466666666666121212121212121244444444444412121212121212121212121212121212121212121212121244444444444488888888
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
χ51111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−ii−i11-1-1i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-111-1-1
χ10111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−ii−i11-1-1i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii−i−iii-1-111-1-111
χ11111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−i−ii-1-111−iiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1-1-111
χ12111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1ii−i−i−ii-1-111−iiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiii−i−i-1-11111-1-1
χ13111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iiii−i-1-111i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−iii-1-11111-1-1
χ14111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iiii−i-1-111i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1-1-111
χ15111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−ii11-1-1−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−iii−i−i-1-111-1-111
χ16111-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1111-1-11111-1-1-1-1−i−iii−ii11-1-1−ii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000002-22-200000000000000000022-2-222-2-200000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000-22-22000000000000000000-2-222-2-22200000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-21111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000002-22-200−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000002-22-200i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000-22-2200−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000-22-2200i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000000000
χ2722222222-2-2-2-222-222-2-22-22222222-2-2-2-222-2-222-2-20000220000-2-2000000002-22-22-22-20000000000000000000000000000
χ2822222222-2-2-2-222-222-2-22-22222222-2-2-2-222-2-222-2-20000-2-200002200000000-22-22-22-220000000000000000000000000000
χ2922222222-2-2-2-22-22-2-222-222222222-2-2-2-2-2-222-2-2222-22-2000000002-22-22-22-2000000000000000000000000000000000000
χ3022222222-2-2-2-22-22-2-222-222222222-2-2-2-2-2-222-2-222-22-2200000000-22-22-22-22000000000000000000000000000000000000
χ3122222222-2-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-1-111-1-1110000220000-2-2−i3i3i3−i3−i3i3i3−i3-11-11-11-11−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3222222222-2-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-1-111-1-1110000220000-2-2i3−i3−i3i3i3−i3−i3i3-11-11-11-11i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3322222222-2-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-1-111-1-1110000-2-2000022−i3i3i3−i3−i3i3i3−i31-11-11-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3422222222-2-2-2-2-12-222-2-22-2-1-1-1-1-1-1-11111-1-111-1-1110000-2-2000022i3−i3−i3i3i3−i3−i3i31-11-11-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3522222222-2-2-2-2-1-22-2-222-22-1-1-1-1-1-1-1111111-1-111-1-12-22-200000000-11-11-11-11−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ3622222222-2-2-2-2-1-22-2-222-22-1-1-1-1-1-1-1111111-1-111-1-12-22-200000000-11-11-11-11i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3722222222-2-2-2-2-1-22-2-222-22-1-1-1-1-1-1-1111111-1-111-1-1-22-22000000001-11-11-11-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3822222222-2-2-2-2-1-22-2-222-22-1-1-1-1-1-1-1111111-1-111-1-1-22-22000000001-11-11-11-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ39222-2-2-22-222-2-22-2-22222-2-222-2-2-2-2222-2-2-2-2-2-222220000002-2-2200000000000000000022-2-2-2-22200000000000000000000
χ40222-2-2-22-222-2-22-2-22222-2-222-2-2-2-2222-2-2-2-2-2-22222000000-222-2000000000000000000-2-22222-2-200000000000000000000
χ41222-2-2-22-222-2-2-122-2-2-2-222-1-11111-1-1-111-1-1-1-111112i2i−2i−2i2i−2i22-2-22i−2i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111100000000000000000000
χ42222-2-2-22-222-2-2-122-2-2-2-222-1-11111-1-1-111-1-1-1-111112i2i−2i−2i−2i2i-2-222−2i2i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-100000000000000000000
χ43222-2-2-22-222-2-2-122-2-2-2-222-1-11111-1-1-111-1-1-1-11111−2i−2i2i2i2i−2i-2-2222i−2iiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-100000000000000000000
χ44222-2-2-22-222-2-2-122-2-2-2-222-1-11111-1-1-111-1-1-1-11111−2i−2i2i2i−2i2i22-2-2−2i2iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111100000000000000000000
χ45222-2-2-22-222-2-2-1-2-22222-2-2-1-11111-1-1-1111111-1-1-1-10000002-2-220033−3−3−3−33333−3−3−3−333-1-11111-1-100000000000000000000
χ46222-2-2-22-222-2-2-1-2-22222-2-2-1-11111-1-1-1111111-1-1-1-10000002-2-2200−3−33333−3−3−3−33333−3−3-1-11111-1-100000000000000000000
χ47222-2-2-22-222-2-2-1-2-22222-2-2-1-11111-1-1-1111111-1-1-1-1000000-222-20033−3−3−3−333−3−33333−3−311-1-1-1-11100000000000000000000
χ48222-2-2-22-222-2-2-1-2-22222-2-2-1-11111-1-1-1111111-1-1-1-1000000-222-200−3−33333−3−333−3−3−3−33311-1-1-1-11100000000000000000000
χ49222-2-2-22-2-2-22222-2-2-2222-222-2-2-2-22-2-22222-2-2-2-22200002i−2i0000−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ50222-2-2-22-2-2-22222-2-2-2222-222-2-2-2-22-2-22222-2-2-2-2220000−2i2i00002i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ51222-2-2-22-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-22222-2-22i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ52222-2-2-22-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-22222-2-2−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ53222-2-2-22-2-2-222-12-2-2-2222-2-1-11111-111-1-1-1-11111-1-100002i−2i0000−2i2i3−3−33−333−3−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i300000000000000000000
χ54222-2-2-22-2-2-222-12-2-2-2222-2-1-11111-111-1-1-1-11111-1-100002i−2i0000−2i2i−333−33−3−33−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i300000000000000000000
χ55222-2-2-22-2-2-222-12-2-2-2222-2-1-11111-111-1-1-1-11111-1-10000−2i2i00002i−2i3−3−33−333−3i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i300000000000000000000
χ56222-2-2-22-2-2-222-12-2-2-2222-2-1-11111-111-1-1-1-11111-1-10000−2i2i00002i−2i−333−33−3−33i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i300000000000000000000
χ57222-2-2-22-2-2-222-1-2222-2-2-22-1-11111-111-1-111-1-1-1-1112i−2i−2i2i00000000−ii−iii−ii−i3−3−33−333−3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ58222-2-2-22-2-2-222-1-2222-2-2-22-1-11111-111-1-111-1-1-1-1112i−2i−2i2i00000000−ii−iii−ii−i−333−33−3−33i3−i3−i3i3−i3i3i3−i300000000000000000000
χ59222-2-2-22-2-2-222-1-2222-2-2-22-1-11111-111-1-111-1-1-1-111−2i2i2i−2i00000000i−ii−i−ii−ii3−3−33−333−3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ60222-2-2-22-2-2-222-1-2222-2-2-22-1-11111-111-1-111-1-1-1-111−2i2i2i−2i00000000i−ii−i−ii−ii−333−33−3−33−i3i3i3−i3i3−i3−i3i300000000000000000000
χ612-2-222-22-22-22-222-22-22-2-22-2-222-2-222-22-22-22-22-22-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ622-2-222-22-22-22-222-22-22-2-22-2-222-2-222-22-22-22-22-22-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ632-2-222-22-22-22-22-22-22-222-2-2-222-2-222-22-2-22-22-22-22000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ642-2-222-22-22-22-22-22-22-222-2-2-222-2-222-22-2-22-22-22-2200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ652-2-222-22-2-22-222222-2-22-2-2-2-222-2-22-22-222-2-222-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ662-2-222-22-2-22-222222-2-22-2-2-2-222-2-22-22-222-2-222-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ672-2-222-22-2-22-222-2-2-222-222-2-222-2-22-22-22-222-2-222-20000000000000000000000000000000000000000000000002-22-20000
χ682-2-222-22-2-22-222-2-2-222-222-2-222-2-22-22-22-222-2-222-2000000000000000000000000000000000000000000000000-22-220000
χ692-2-2-2-22222-2-2222-2-22-22-22-2-2-2-22222-2-222-22-2-22-2200000000000000000000000000000000000022-2-2-2-222000000000000
χ702-2-2-2-22222-2-2222-2-22-22-22-2-2-2-22222-2-222-22-2-22-22000000000000000000000000000000000000-2-22222-2-2000000000000
χ712-2-2-2-22222-2-222-222-22-22-2-2-2-2-22222-2-22-22-222-22-2000000000000000000000000000000000000000000002-2-2200000000
χ722-2-2-2-22222-2-222-222-22-22-2-2-2-2-22222-2-22-22-222-22-200000000000000000000000000000000000000000000-222-200000000
χ732-2-2-2-2222-222-2222-222-2-2-2-2-2-2-2222-222-22-2-22-222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ742-2-2-2-2222-222-2222-222-2-2-2-2-2-2-2222-222-22-2-22-222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ752-2-2-2-2222-222-22-2-22-2-2222-2-2-2-2222-222-2-222-22-2-220000000000000000000000000000000000000000000000002-2-220000
χ762-2-2-2-2222-222-22-2-22-2-2222-2-2-2-2222-222-2-222-22-2-22000000000000000000000000000000000000000000000000-222-20000
χ7744-44-44-4-400004000000004-44-44-4-40000000000000000000000000000000000000000000000002-22-22-22-2000000000000
χ7844-44-44-4-400004000000004-44-44-4-4000000000000000000000000000000000000000000000000-22-22-22-22000000000000
χ7944-4-44-4-4400004000000004-4-44-44-40000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ8044-4-44-4-4400004000000004-4-44-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ814-444-4-4-440000400000000-444-4-44-40000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ824-444-4-4-440000400000000-444-4-44-4000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ834-44-444-4-40000400000000-44-444-4-40000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ844-44-444-4-40000400000000-44-444-4-4000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ854-4-444-44-44-44-4-24-44-44-4-4422-2-222-2-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ864-4-444-44-44-44-4-2-44-44-444-422-2-222-2-22-222-22-22-22-200000000000000000000000000000000000000000000000000000000
χ874-4-444-44-4-44-44-2444-4-44-4-422-2-222-22-22-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ884-4-444-44-4-44-44-2-4-4-444-44422-2-222-22-22-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-4-4-44444-4-44-24-4-44-44-442222-2-2-2-222-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ904-4-4-4-44444-4-44-2-444-44-44-42222-2-2-2-222-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4444-444-4-244-444-4-4-42222-2-2-22-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-444-4-2-4-44-4-44442222-2-2-22-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ9388-88-88-8-80000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-880000-400000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-8-880000-4000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-888-8-80000-4000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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