Finite Group Databasebeta

← Group #10840269

Character table — Group #10840269

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222222244444444444444444444444444444444888888888888888888888888242424242424242448484848
order1244222344444446668888121212121212121212121212446688888812121212121224242424242424242424242424242424224444446666121212121212121212121212244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1111111-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-111111111-1-111-1-1-11-11
χ8111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ9111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111
χ10111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-111
χ13111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1
χ14111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ15111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-11
χ16111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1
χ172222222-12222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-12222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ192222222-12222222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111112-22-222-2-2-1-111-1-1-1-1-1-1111111000000000000
χ202222222-12222222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-22-22-2-22211-1-1111111-1-1-1-1-1-1000000000000
χ212222222-12-2-2-2-222-1-1-12222-1-1-1-111111111-2-2-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-11111-1-11111000000000000
χ222222222-12-2-2-2-222-1-1-12222-1-1-1-111111111-2-2-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-22222111111-1-1-1-111-1-1-1-1000000000000
χ232222222-12-2-2-2-222-1-1-1-2-2-2-2-1-1-1-111111111-2-2-1-1-2-222221111-1-111111111-1-1-1-1-1-1-1-12-22-2-2-222-1-111-1-1111111-1-1-1-1000000000000
χ242222222-12-2-2-2-222-1-1-1-2-2-2-2-1-1-1-111111111-2-2-1-1-2-222221111-1-111111111-1-1-1-1-1-1-1-1-22-2222-2-211-1-111-1-1-1-1-1-11111000000000000
χ2522222-2-2222222-2-22220000222222222222-2-2-2-2000000-2-2-2-2-2-20000000000000000000000000000000000000000002i−2i002i−2i0000
χ2622222-2-2222222-2-22220000222222222222-2-2-2-2000000-2-2-2-2-2-2000000000000000000000000000000000000000000−2i2i00−2i2i0000
χ2722222-2-222-2-2-2-2-2-222200002222-2-2-2-2-2-2-2-222-2-20000002222-2-20000000000000000000000000000000000000000002i−2i00−2i2i0000
χ2822222-2-222-2-2-2-2-2-222200002222-2-2-2-2-2-2-2-222-2-20000002222-2-2000000000000000000000000000000000000000000−2i2i002i−2i0000
χ292222-22-22-200002-22-2-2222222-2-200000000002-2-2-2000000002-22222-2-2-2-20000000000002i−2i2i−2i0000002i2i−2i−2i002i2i−2i−2i000000000000
χ302222-22-22-200002-22-2-2222222-2-200000000002-2-2-2000000002-22222-2-2-2-2000000000000−2i2i−2i2i000000−2i−2i2i2i00−2i−2i2i2i000000000000
χ312222-22-22-200002-22-2-2-2-2-2-222-2-200000000002-222000000002-2-2-2-2-222220000000000002i−2i−2i2i0000002i2i−2i−2i00−2i−2i2i2i000000000000
χ322222-22-22-200002-22-2-2-2-2-2-222-2-200000000002-222000000002-2-2-2-2-22222000000000000−2i2i2i−2i000000−2i−2i2i2i002i2i−2i−2i000000000000
χ332222-22-2-1-200002-2-1112222-1-1113333−3−3−3−300-11-2-2000033−3−3-11-1-1-1-111113333−3−3−3−300002i−2i2i−2i−i3i3−i3i3−i3i3−i−iii−i3i3−i−iii000000000000
χ342222-22-2-1-200002-2-1112222-1-1113333−3−3−3−300-11-2-2000033−3−3-11-1-1-1-111113333−3−3−3−30000−2i2i−2i2ii3−i3i3−i3i3−i3ii−i−ii3−i3ii−i−i000000000000
χ352222-22-2-1-200002-2-1112222-1-111−3−3−3−3333300-11-2-20000−3−333-11-1-1-1-11111−3−3−3−3333300002i−2i2i−2ii3−i3i3−i3i3−i3−i−iiii3−i3−i−iii000000000000
χ362222-22-2-1-200002-2-1112222-1-111−3−3−3−3333300-11-2-20000−3−333-11-1-1-1-11111−3−3−3−333330000−2i2i−2i2i−i3i3−i3i3−i3i3ii−i−i−i3i3ii−i−i000000000000
χ372222-22-2-1-200002-2-111-2-2-2-2-1-1113333−3−3−3−300-1122000033−3−3-111111-1-1-1-1−3−3−3−3333300002i−2i−2i2i−i3i3i3−i3−i3i3−i−iiii3−i3ii−i−i000000000000
χ382222-22-2-1-200002-2-111-2-2-2-2-1-1113333−3−3−3−300-1122000033−3−3-111111-1-1-1-1−3−3−3−333330000−2i2i2i−2ii3−i3−i3i3i3−i3ii−i−i−i3i3−i−iii000000000000
χ392222-22-2-1-200002-2-111-2-2-2-2-1-111−3−3−3−3333300-11220000−3−333-111111-1-1-1-13333−3−3−3−300002i−2i−2i2ii3−i3−i3i3i3−i3−i−iii−i3i3ii−i−i000000000000
χ402222-22-2-1-200002-2-111-2-2-2-2-1-111−3−3−3−3333300-11220000−3−333-111111-1-1-1-13333−3−3−3−30000−2i2i2i−2i−i3i3i3−i3−i3i3ii−i−ii3−i3−i−iii000000000000
χ4122-2-22-2-22-200002222222-2-2-2-2-2-20000000000-2-22-2000000002222-2-222-2-20000000022-2-200002222-2-20000-2-20000000000000000
χ4222-2-22-2-22-200002222222-2-2-2-2-2-20000000000-2-22-2000000002222-2-222-2-200000000-2-2220000-2-2-2-2220000220000000000000000
χ4322-2-22-2-22-2000022222-2-222-2-2-2-20000000000-2-2-220000000022-2-222-2-222000000002-2-22000022-2-2-2-20000220000000000000000
χ4422-2-22-2-22-2000022222-2-222-2-2-2-20000000000-2-2-220000000022-2-222-2-22200000000-222-20000-2-222220000-2-20000000000000000
χ4522-2-22-2-2-1-2000022-1-1-122-2-21111−i3−i3i3i3−i3−i3i3i300112-20000−i3i3−i3i3-1-1-1-111-1-111−i3−i3i3i3−i3−i3i3i322-2-20000-1-1-1-111−i3i3−i3i311−i3i3−i3i3000000000000
χ4622-2-22-2-2-1-2000022-1-1-122-2-21111−i3−i3i3i3−i3−i3i3i300112-20000−i3i3−i3i3-1-1-1-111-1-111−i3−i3i3i3−i3−i3i3i3-2-22200001111-1-1i3−i3i3−i3-1-1i3−i3i3−i3000000000000
χ4722-2-22-2-2-1-2000022-1-1-122-2-21111i3i3−i3−i3i3i3−i3−i300112-20000i3−i3i3−i3-1-1-1-111-1-111i3i3−i3−i3i3i3−i3−i322-2-20000-1-1-1-111i3−i3i3−i311i3−i3i3−i3000000000000
χ4822-2-22-2-2-1-2000022-1-1-122-2-21111i3i3−i3−i3i3i3−i3−i300112-20000i3−i3i3−i3-1-1-1-111-1-111i3i3−i3−i3i3i3−i3−i3-2-22200001111-1-1−i3i3−i3i3-1-1−i3i3−i3i3000000000000
χ4922-2-22-2-2-1-2000022-1-1-1-2-2221111−i3−i3i3i3−i3−i3i3i30011-220000−i3i3−i3i3-1-111-1-111-1-1i3i3−i3−i3i3i3−i3−i32-2-220000-1-11111−i3i3−i3i3-1-1i3−i3i3−i3000000000000
χ5022-2-22-2-2-1-2000022-1-1-1-2-2221111−i3−i3i3i3−i3−i3i3i30011-220000−i3i3−i3i3-1-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3-222-2000011-1-1-1-1i3−i3i3−i311−i3i3−i3i3000000000000
χ5122-2-22-2-2-1-2000022-1-1-1-2-2221111i3i3−i3−i3i3i3−i3−i30011-220000i3−i3i3−i3-1-111-1-111-1-1−i3−i3i3i3−i3−i3i3i32-2-220000-1-11111i3−i3i3−i3-1-1−i3i3−i3i3000000000000
χ5222-2-22-2-2-1-2000022-1-1-1-2-2221111i3i3−i3−i3i3i3−i3−i30011-220000i3−i3i3−i3-1-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3-222-2000011-1-1-1-1−i3i3−i3i311i3−i3i3−i3000000000000
χ5322-2-2-22-2222i2i−2i−2i-222-2-20000-2-2222i2i−2i−2i−2i−2i2i2i2i−2i2-2000000−2i2i2i−2i-2200000000000000000000000000000000000000002-2002i−2i000000
χ5422-2-2-22-2222i2i−2i−2i-222-2-20000-2-2222i2i−2i−2i−2i−2i2i2i2i−2i2-2000000−2i2i2i−2i-220000000000000000000000000000000000000000-2200−2i2i000000
χ5522-2-2-22-222−2i−2i2i2i-222-2-20000-2-222−2i−2i2i2i2i2i−2i−2i−2i2i2-20000002i−2i−2i2i-2200000000000000000000000000000000000000002-200−2i2i000000
χ5622-2-2-22-222−2i−2i2i2i-222-2-20000-2-222−2i−2i2i2i2i2i−2i−2i−2i2i2-20000002i−2i−2i2i-220000000000000000000000000000000000000000-22002i−2i000000
χ5722-2-2-2-22222i2i−2i−2i2-22-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i2i-22-222i2i−2i−2i2i−2i−2i2i2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ5822-2-2-2-22222i2i−2i−2i2-22-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i−2i2i-222-2−2i−2i2i2i2i−2i−2i2i2-2-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ5922-2-2-2-2222−2i−2i2i2i2-22-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i−2i-22-22−2i−2i2i2i−2i2i2i−2i2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ6022-2-2-2-2222−2i−2i2i2i2-22-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i2i−2i-222-22i2i−2i−2i−2i2i2i−2i2-2-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ6122-2-2-2-22-122i2i−2i−2i2-2-11122-2-211-1-1−i−iiiii−i−i−2i2i1-1-222i2i−2i−2i−iii−i-11-1-11111-1-1−i−iiiii−i−i00000000−i3i3−i3i3i3−i33−3−33i3−i33−3−33000000000000
χ6222-2-2-2-22-122i2i−2i−2i2-2-11122-2-211-1-1−i−iiiii−i−i−2i2i1-1-222i2i−2i−2i−iii−i-11-1-11111-1-1−i−iiiii−i−i00000000i3−i3i3−i3−i3i3−333−3−i3i3−333−3000000000000
χ6322-2-2-2-22-122i2i−2i−2i2-2-111-2-22211-1-1−i−iiiii−i−i−2i2i1-12-2−2i−2i2i2i−iii−i-1111-1-1-1-111ii−i−i−i−iii00000000−i3i3i3−i3i3−i33−3−33−i3i3−333−3000000000000
χ6422-2-2-2-22-122i2i−2i−2i2-2-111-2-22211-1-1−i−iiiii−i−i−2i2i1-12-2−2i−2i2i2i−iii−i-1111-1-1-1-111ii−i−i−i−iii00000000i3−i3−i3i3−i3i3−333−3i3−i33−3−33000000000000
χ6522-2-2-2-22-12−2i−2i2i2i2-2-11122-2-211-1-1ii−i−i−i−iii2i−2i1-1-22−2i−2i2i2ii−i−ii-11-1-11111-1-1ii−i−i−i−iii00000000−i3i3−i3i3i3−i3−333−3i3−i3−333−3000000000000
χ6622-2-2-2-22-12−2i−2i2i2i2-2-11122-2-211-1-1ii−i−i−i−iii2i−2i1-1-22−2i−2i2i2ii−i−ii-11-1-11111-1-1ii−i−i−i−iii00000000i3−i3i3−i3−i3i33−3−33−i3i33−3−33000000000000
χ6722-2-2-2-22-12−2i−2i2i2i2-2-111-2-22211-1-1ii−i−i−i−iii2i−2i1-12-22i2i−2i−2ii−i−ii-1111-1-1-1-111−i−iiiii−i−i00000000−i3i3i3−i3i3−i3−333−3−i3i33−3−33000000000000
χ6822-2-2-2-22-12−2i−2i2i2i2-2-111-2-22211-1-1ii−i−i−i−iii2i−2i1-12-22i2i−2i−2ii−i−ii-1111-1-1-1-111−i−iiiii−i−i00000000i3−i3−i3i3−i3i33−3−33i3−i3−333−3000000000000
χ6944444-4-4-244444-4-4-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2-4-4220000002222220000000000000000000000000000000000000000000000000000
χ7044444-4-4-24-4-4-4-4-4-4-2-2-20000-2-2-2-2222222224422000000-2-2-2-2220000000000000000000000000000000000000000000000000000
χ714444-4-444-40000-444-4-4000044-4-40000000000-440000000000-440000000000000000000000000000000000000000000000000000
χ724444-4-44-2-40000-44-2220000-2-22223232323−23−23−23−23002-2000000−23−2323232-20000000000000000000000000000000000000000000000000000
χ734444-4-44-2-40000-44-2220000-2-222−23−23−23−2323232323002-20000002323−23−232-20000000000000000000000000000000000000000000000000000
χ7444-4-44444-40000-4-44440000-4-4-4-40000000000440000000000-4-40000000000000000000000000000000000000000000000000000
χ7544-4-4444-2-40000-4-4-2-2-200002222−2i3−2i32i32i3−2i3−2i32i32i300-2-20000002i3−2i32i3−2i3220000000000000000000000000000000000000000000000000000
χ7644-4-4444-2-40000-4-4-2-2-2000022222i32i3−2i3−2i32i32i3−2i3−2i300-2-2000000−2i32i3−2i32i3220000000000000000000000000000000000000000000000000000
χ7744-4-4-44-4-244i4i−4i−4i-44-222000022-2-2−2i−2i2i2i2i2i−2i−2i4i−4i-220000002i−2i−2i2i2-20000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.