Finite Group Databasebeta

← Group #10691613

Character table — Group #10691613

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222222223446666666444444444446666121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-1-1-11111-1-11-1-1111-1-11-1ii−i−i-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-11-1i−iii−i−iii−i−i1-1iiii−i−i−i−i11-1-111-1-1ii−i−i1-1i−i
χ10111111-1-1-1-11111-1-11-1-1111-1-11-1ii−i−i-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-11-1i−iii−i−iii−i−i1-1iiii−i−i−i−i11-1-1-1-111−i−iii-11−ii
χ11111111-1-1-1-11111-1-11-1-1111-1-11-1−i−iii-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii−i−iii−i−iii1-1−i−i−i−iiiii11-1-111-1-1−i−iii1-1−ii
χ12111111-1-1-1-11111-1-11-1-1111-1-11-1−i−iii-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii−i−iii−i−iii1-1−i−i−i−iiiii11-1-1-1-111ii−i−i-11i−i
χ13111111-1-1-1-11111-1-11-1-11-1-1111-1ii−i−i-111-1-111-1-1iiii−i−i−i−i-1-1-1-11111-11i−i−i−iiiii−i−i1-1−i−i−i−iiiii-1-11111-1-1ii−i−i-11−ii
χ14111111-1-1-1-11111-1-11-1-11-1-1111-1ii−i−i-111-1-111-1-1iiii−i−i−i−i-1-1-1-11111-11i−i−i−iiiii−i−i1-1−i−i−i−iiiii-1-111-1-111−i−iii1-1i−i
χ15111111-1-1-1-11111-1-11-1-11-1-1111-1−i−iii-111-1-111-1-1−i−i−i−iiiii-1-1-1-11111-11−iiii−i−i−i−iii1-1iiii−i−i−i−i-1-11111-1-1−i−iii-11i−i
χ16111111-1-1-1-11111-1-11-1-11-1-1111-1−i−iii-111-1-111-1-1−i−i−i−iiiii-1-1-1-11111-11−iiii−i−i−i−iii1-1iiii−i−i−i−i-1-111-1-111ii−i−i1-1−ii
χ1722222222222-2-222222220000-2-22222-22222-2-2-2-2222222220000000000-2-20000-2-2-2-2-2-2000000000000000000000000
χ1822222222222-2-222222220000-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000002200002222-2-2000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222222-122-1-1-1-1-1-1-1222222-2-2-2-22-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2-2-21111-1-111111111-1-1-1-1000000000000
χ212222222222-122-1-1-1-1-1-1-1-2-2-2-22222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ222222222222-122-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22-1-1-1-1-1-1-1-11111111111111111-2-2-2-222221111-1-1-1-1-1-1-1-1-1-11111000000000000
χ232222222222-1-2-2-1-1-1-1-1-1-10000-2-22222-2-1-1-1-11111-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300-2-20000111111−i3−i3i3i3−i3−i3i3i3−i3i3−i3i3000000000000
χ242222222222-1-2-2-1-1-1-1-1-1-10000-2-22222-2-1-1-1-11111-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300-2-20000111111i3i3−i3−i3i3i3−i3−i3i3−i3i3−i3000000000000
χ252222222222-1-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-1-1-1-1111111111111−i3−i3i3i3−i3−i3i3i300220000-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3i3−i3i3000000000000
χ262222222222-1-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-1-1-1-1111111111111i3i3−i3−i3i3i3−i3−i300220000-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3−i3i3−i3000000000000
χ27222222-2-2-2-22-2-22-2-22-2-220000-222i2i−2i−2i222-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000−2i2i0000−2i−2i2i2i-22000000000000000000000000
χ28222222-2-2-2-22-2-22-2-22-2-220000-22−2i−2i2i2i222-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000002i−2i00002i2i−2i−2i-22000000000000000000000000
χ29222222-2-2-2-2-122-111-111-122-2-22-22i2i−2i−2i-2-1-111-1-111−i−i−i−iiiii-1-1-1-111112-22i−2i2i2i−2i−2i−i−iii-11−i−i−i−iiiii-1-111000000000000
χ30222222-2-2-2-2-122-111-111-122-2-22-2−2i−2i2i2i-2-1-111-1-111iiii−i−i−i−i-1-1-1-111112-2−2i2i−2i−2i2i2iii−i−i-11iiii−i−i−i−i-1-111000000000000
χ31222222-2-2-2-2-122-111-111-1-2-2222-22i2i−2i−2i-2-1-111-1-111−i−i−i−iiiii1111-1-1-1-1-222i−2i−2i−2i2i2i−i−iii-11iiii−i−i−i−i11-1-1000000000000
χ32222222-2-2-2-2-122-111-111-1-2-2222-2−2i−2i2i2i-2-1-111-1-111iiii−i−i−i−i1111-1-1-1-1-22−2i2i2i2i−2i−2iii−i−i-11−i−i−i−iiiii11-1-1000000000000
χ33222222-2-2-2-2-1-2-2-111-111-10000-222i2i−2i−2i2-1-11111-1-1−i−i−i−iiiii−i3−i3i3i3i3i3−i3−i300−2i2i0000ii−i−i1-133−3−3−3−333−i3i3i3−i3000000000000
χ34222222-2-2-2-2-1-2-2-111-111-10000-222i2i−2i−2i2-1-11111-1-1−i−i−i−iiiiii3i3−i3−i3−i3−i3i3i300−2i2i0000ii−i−i1-1−3−33333−3−3i3−i3−i3i3000000000000
χ35222222-2-2-2-2-1-2-2-111-111-10000-22−2i−2i2i2i2-1-11111-1-1iiii−i−i−i−i−i3−i3i3i3i3i3−i3−i3002i−2i0000−i−iii1-1−3−33333−3−3−i3i3i3−i3000000000000
χ36222222-2-2-2-2-1-2-2-111-111-10000-22−2i−2i2i2i2-1-11111-1-1iiii−i−i−i−ii3i3−i3−i3−i3−i3i3i3002i−2i0000−i−iii1-133−3−3−3−333i3−i3−i3i3000000000000
χ372222-2-22-2-222222-2-22-2-2222-2-2-2-200002-2-22222-2-2000000002222-2-2-2-2-220000000000-2200000000-2-222000000000000
χ382222-2-22-2-222222-2-22-2-22-2-222-2-200002-2-22222-2-200000000-2-2-2-222222-20000000000-220000000022-2-2000000000000
χ392222-2-22-2-222-2-22-2-22-2-220000220000-2-2-222-2-222000000000000000000002i−2i2i−2i00002-22i−2i2i−2i2i−2i2i−2i0000000000000000
χ402222-2-22-2-222-2-22-2-22-2-220000220000-2-2-222-2-22200000000000000000000−2i2i−2i2i00002-2−2i2i−2i2i−2i2i−2i2i0000000000000000
χ412222-2-22-2-22-122-111-111-122-2-2-2-20000211-1-1-1-11133−3−333−3−3-1-1-1-11111-220000003−33−31-13−3−333−3−3311-1-1000000000000
χ422222-2-22-2-22-122-111-111-122-2-2-2-20000211-1-1-1-111−3−333−3−333-1-1-1-11111-22000000−33−331-1−333−3−333−311-1-1000000000000
χ432222-2-22-2-22-122-111-111-1-2-222-2-20000211-1-1-1-11133−3−333−3−31111-1-1-1-12-20000003−33−31-1−333−3−333−3-1-111000000000000
χ442222-2-22-2-22-122-111-111-1-2-222-2-20000211-1-1-1-111−3−333−3−3331111-1-1-1-12-2000000−33−331-13−3−333−3−33-1-111000000000000
χ452222-2-22-2-22-1-2-2-111-111-10000220000-211-1-111-1-133−3−333−3−3−i3−i3i3i3i3i3−i3−i300002i−2i2i−2i−33−33-11−ii−ii−ii−iii3−i3−i3i3000000000000
χ462222-2-22-2-22-1-2-2-111-111-10000220000-211-1-111-1-133−3−333−3−3i3i3−i3−i3−i3−i3i3i30000−2i2i−2i2i−33−33-11i−ii−ii−ii−i−i3i3i3−i3000000000000
χ472222-2-22-2-22-1-2-2-111-111-10000220000-211-1-111-1-1−3−333−3−333−i3−i3i3i3i3i3−i3−i30000−2i2i−2i2i3−33−3-11i−ii−ii−ii−ii3−i3−i3i3000000000000
χ482222-2-22-2-22-1-2-2-111-111-10000220000-211-1-111-1-1−3−333−3−333i3i3−i3−i3−i3−i3i3i300002i−2i2i−2i3−33−3-11−ii−ii−ii−ii−i3i3i3−i3000000000000
χ492222-2-2-222-222222222222222-220000-2-2-2-2-222220000000022222222-2-20000000000-2-200000000-2-2-2-2000000000000
χ502222-2-2-222-22222222222-2-2-2-2-220000-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2220000000000-2-2000000002222000000000000
χ512222-2-2-222-22-2-2222222200002-200002-2-2-2-2-2-2-2-2000000000000000000002-2-220000222-22-2-22-220000000000000000
χ522222-2-2-222-22-2-2222222200002-200002-2-2-2-2-2-2-2-200000000000000000000-222-2000022-22-222-22-20000000000000000
χ532222-2-2-222-2-122-1-1-1-1-1-1-12222-220000-21111-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1-1-1-2-2000000−i3i3i3−i311−i3i3i3−i3i3−i3−i3i31111000000000000
χ542222-2-2-222-2-122-1-1-1-1-1-1-12222-220000-21111-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1-1-1-2-2000000i3−i3−i3i311i3−i3−i3i3−i3i3i3−i31111000000000000
χ552222-2-2-222-2-122-1-1-1-1-1-1-1-2-2-2-2-220000-21111-1-1-1-1−i3−i3i3i3i3i3−i3−i31111111122000000−i3i3i3−i311i3−i3−i3i3−i3i3i3−i3-1-1-1-1000000000000
χ562222-2-2-222-2-122-1-1-1-1-1-1-1-2-2-2-2-220000-21111-1-1-1-1i3i3−i3−i3−i3−i3i3i31111111122000000i3−i3−i3i311−i3i3i3−i3i3−i3−i3i3-1-1-1-1000000000000
χ572222-2-2-222-2-1-2-2-1-1-1-1-1-1-100002-20000211111111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300002-2-22i3−i3−i3i3-1-1-11-111-11-1i3−i3i3−i3000000000000
χ582222-2-2-222-2-1-2-2-1-1-1-1-1-1-100002-20000211111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000-222-2i3−i3−i3i3-1-11-11-1-11-11−i3i3−i3i3000000000000
χ592222-2-2-222-2-1-2-2-1-1-1-1-1-1-100002-20000211111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000-222-2−i3i3i3−i3-1-11-11-1-11-11i3−i3i3−i3000000000000
χ602222-2-2-222-2-1-2-2-1-1-1-1-1-1-100002-20000211111111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300002-2-22−i3i3i3−i3-1-1-11-111-11-1−i3i3−i3i3000000000000
χ6122-2-22-22-22-2200-2-2-2-22220000002-22-202-22-200002-22-22-22-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ6222-2-22-22-22-2200-2-2-2-22220000002-22-202-22-200002-22-22-22-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ6322-2-22-22-22-2200-2-2-2-2222000000-22-2202-22-20000-22-22-22-220000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ6422-2-22-22-22-2200-2-2-2-2222000000-22-2202-22-20000-22-22-22-220000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ6522-2-22-2-22-22200-222-2-2-220000002i−2i−2i2i02-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−i2i2i2−i22−2−220000
χ6622-2-22-2-22-22200-222-2-2-220000002i−2i−2i2i02-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000i2−i2−i2i2−222−20000
χ6722-2-22-2-22-22200-222-2-2-22000000−2i2i2i−2i02-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−i2i2i2−i2−222−20000
χ6822-2-22-2-22-22200-222-2-2-22000000−2i2i2i−2i02-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000i2−i2−i2i22−2−220000
χ6944-4-44-44-44-4-2002222-2-2-20000004-44-40-22-220000-22-22-22-220000000000000000000000000000000000000000000000
χ7044-4-44-44-44-4-2002222-2-2-2000000-44-440-22-2200002-22-22-22-20000000000000000000000000000000000000000000000
χ7144-4-44-4-44-44-2002-2-2222-20000004i−4i−4i4i0-222-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7244-4-44-4-44-44-2002-2-2222-2000000−4i4i4i−4i0-222-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7344-4-4-4444-4-4400-444-4-4-4400000000000-444-40000000000000000000000000000000000000000000000000000000000
χ7444-4-4-4444-4-4-2002-2-2222-2000000000002-2-22000023−23−232323−23−23230000000000000000000000000000000000000000000000
χ7544-4-4-4444-4-4-2002-2-2222-2000000000002-2-220000−232323−23−232323−230000000000000000000000000000000000000000000000
χ7644-4-4-44-4-444400-4-4-4-444400000000000-44-440000000000000000000000000000000000000000000000000000000000
χ7744-4-4-44-4-444-2002222-2-2-2000000000002-22-20000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7844-4-4-44-4-444-2002222-2-2-2000000000002-22-200002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ794-4-4400000044-4-400400-4004i−4i000000000004-4000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ804-4-4400000044-4-400400-400−4i4i000000000004-400000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ814-4-440000004-44-400400-44i−4i0000000000000-4400000000004i−4i4i−4i000000000000000000000000000000000000000000
χ824-4-440000004-44-400400-4−4i4i0000000000000-440000000000−4i4i−4i4i000000000000000000000000000000000000000000
χ834-4-44000000-24-42−2i32i3-2−2i32i32004i−4i00000000000-22−2i32i30000000023−23−2323−2i2i−2i2i00000000000000000000000000000000000000
χ844-4-44000000-24-42−2i32i3-2−2i32i3200−4i4i00000000000-22−2i32i300000000−232323−232i−2i2i−2i00000000000000000000000000000000000000
χ854-4-44000000-24-422i3−2i3-22i3−2i32004i−4i00000000000-222i3−2i300000000−232323−23−2i2i−2i2i00000000000000000000000000000000000000
χ864-4-44000000-24-422i3−2i3-22i3−2i3200−4i4i00000000000-222i3−2i30000000023−23−23232i−2i2i−2i00000000000000000000000000000000000000
χ874-4-44000000-2-442−2i32i3-2−2i32i324i−4i00000000000002-22i3−2i300000000−2i2i−2i2i23−23−232300000000000000000000000000000000000000
χ884-4-44000000-2-442−2i32i3-2−2i32i32−4i4i00000000000002-22i3−2i3000000002i−2i2i−2i−232323−2300000000000000000000000000000000000000
χ894-4-44000000-2-4422i3−2i3-22i3−2i324i−4i00000000000002-2−2i32i300000000−2i2i−2i2i−232323−2300000000000000000000000000000000000000
χ904-4-44000000-2-4422i3−2i3-22i3−2i32−4i4i00000000000002-2−2i32i3000000002i−2i2i−2i23−23−232300000000000000000000000000000000000000
χ918-88-8000000800800-800-80000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-8000000-400-4−4i34i344i3−4i340000000000000000000000000000000000000000000000000000000000000000000000000
χ938-88-8000000-400-44i3−4i34−4i34i340000000000000000000000000000000000000000000000000000000000000000000000000

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