Finite Group Databasebeta

← Group #10831007

Character table — Group #10831007

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222244444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order12222222344446666666121212121212121222444444888888881212121212121212242424242424242424242424242424242466668888121212122424242424242424222222444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ91111111111111111111111111111-1-11111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ101111111111111111111111111111-1-11111-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-111-1
χ121111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-11-1-11
χ131111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-11111-1-1-111-1
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1
χ161111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ17222222222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002222-2-2-2-200000000000000002-222220000-2-2-2-200000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-200000000-2-2-2-222220000000000000000-2222-2-20000-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222000000002222-2-2-2-20000000000000000-22-2-2-2-20000222200000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2222200000000000000002-2-2-222000022-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2222222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-1-11122-2-2-1-111-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-2-1-111-2-222-1-1111111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-2111111111111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112211-1-1-2-22211-1-11111-1-1-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12211-1-122-2-211-1-1-1-1-1-11111000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−32-2-1-1-1-10000111133−3−333−3−3000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333332-2-1-1-1-100001111−3−333−3−333000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-22-1-111000011-1-133−3−3−3−333000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-22-1-111000011-1-1−3−33333−3−3000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-22200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-2211110000-1-1-1-1−3−333−3−333000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-22200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-2211110000-1-1-1-133−3−333−3−3000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-211-1-10000-1-111−3−33333−3−3000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-211-1-10000-1-11133−3−3−3−333000000000000
χ3722-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-22200000000000022-2-2000000000000000022-2-222-2-20000000000000000000000002-2002-20000
χ3822-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-22200000000000022-2-2000000000000000022-2-222-2-2000000000000000000000000-2200-220000
χ3922-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-222000000000000-2-2220000000000000000-2-222-2-2220000000000000000000000002-200-220000
χ4022-2-2-2-22222-2-2222-2-2-2-2222-2-2-2-222000000000000-2-2220000000000000000-2-222-2-222000000000000000000000000-22002-20000
χ412-222-2-22-2222-2-2-2-2-2-22222222-2-2-2-22-200002-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000002-2002i−2i002-2002i−2i2i−2i0000000000000000
χ422-222-2-22-2222-2-2-2-2-2-22222222-2-2-2-22-200002-2−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000002-200−2i2i002-200−2i2i−2i2i0000000000000000
χ432-222-2-22-2222-2-2-2-2-2-22222222-2-2-2-2-220000-222i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000-2200−2i2i00-2200−2i2i−2i2i0000000000000000
χ442-222-2-22-2222-2-2-2-2-2-22222222-2-2-2-2-220000-22−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000-22002i−2i00-22002i−2i2i−2i0000000000000000
χ452-222-2-22-22-2-222-2-2-2-2222-2-2-2-222222-20000-2200002-22-200000000000000002-22-22-22-2002-200002-2-220000002-22-2000000000000
χ462-222-2-22-22-2-222-2-2-2-2222-2-2-2-222222-20000-220000-22-220000000000000000-22-22-22-22002-20000-22-22000000-22-22000000000000
χ472-222-2-22-22-2-222-2-2-2-2222-2-2-2-22222-2200002-200002-22-200000000000000002-22-22-22-200-220000-222-2000000-22-22000000000000
χ482-222-2-22-22-2-222-2-2-2-2222-2-2-2-22222-2200002-20000-22-220000000000000000-22-22-22-2200-2200002-22-20000002-22-2000000000000
χ492-222-2-22-2-122-2-21111-1-1-1-1-1-1-111112-200002-22i2i−2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii3−33−3−33−3300-11−i3i32i−2i00-11−i3i3−ii−ii3−3−33000000000000
χ502-222-2-22-2-122-2-21111-1-1-1-1-1-1-111112-200002-22i2i−2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−33−333−33−300-11i3−i32i−2i00-11i3−i3−ii−ii−333−3000000000000
χ512-222-2-22-2-122-2-21111-1-1-1-1-1-1-111112-200002-2−2i−2i2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−33−333−33−300-11−i3i3−2i2i00-11−i3i3i−ii−i−333−3000000000000
χ522-222-2-22-2-122-2-21111-1-1-1-1-1-1-111112-200002-2−2i−2i2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i3−33−3−33−3300-11i3−i3−2i2i00-11i3−i3i−ii−i3−3−33000000000000
χ532-222-2-22-2-122-2-21111-1-1-1-1-1-1-11111-220000-222i2i−2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii3−33−3−33−33001-1i3−i3−2i2i001-1i3−i3i−ii−i−333−3000000000000
χ542-222-2-22-2-122-2-21111-1-1-1-1-1-1-11111-220000-222i2i−2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−33−333−33−3001-1−i3i3−2i2i001-1−i3i3i−ii−i3−3−33000000000000
χ552-222-2-22-2-122-2-21111-1-1-1-1-1-1-11111-220000-22−2i−2i2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−33−333−33−3001-1i3−i32i−2i001-1i3−i3−ii−ii3−3−33000000000000
χ562-222-2-22-2-122-2-21111-1-1-1-1-1-1-11111-220000-22−2i−2i2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i3−33−3−33−33001-1−i3i32i−2i001-1−i3i3−ii−ii−333−3000000000000
χ572-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-12-20000-2200002-22-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-11-11-11-1100-11−i3i3002-21-1i3−i3−i3i3i3−i3-11-11000000000000
χ582-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-12-20000-2200002-22-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-11-11-11-1100-11i3−i3002-21-1−i3i3i3−i3−i3i3-11-11000000000000
χ592-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-12-20000-220000-22-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-11-11-11-100-11−i3i300-221-1i3−i3i3−i3−i3i31-11-1000000000000
χ602-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-12-20000-220000-22-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-11-11-11-100-11i3−i300-221-1−i3i3−i3i3i3−i31-11-1000000000000
χ612-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-1-2200002-200002-22-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-11-11-11-11001-1i3−i300-22-11−i3i3i3−i3−i3i31-11-1000000000000
χ622-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-1-2200002-200002-22-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-11-11-11-11001-1−i3i300-22-11i3−i3−i3i3i3−i31-11-1000000000000
χ632-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-1-2200002-20000-22-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-11-11-11-1001-1i3−i3002-2-11−i3i3−i3i3i3−i3-11-11000000000000
χ642-222-2-22-2-1-2-2221111-1-1-11111-1-1-1-1-2200002-20000-22-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-11-11-11-1001-1−i3i3002-2-11i3−i3i3−i3−i3i3-11-11000000000000
χ652-2-2-2222-22-22-22-2-222-2-22-2-222-2-2220000000000002-2-2200000000000000002-2-222-2-2200000000000000000000002-2002-2000000
χ662-2-2-2222-22-22-22-2-222-2-22-2-222-2-2220000000000002-2-2200000000000000002-2-222-2-220000000000000000000000-2200-22000000
χ672-2-2-2222-22-22-22-2-222-2-22-2-222-2-222000000000000-222-20000000000000000-222-2-222-200000000000000000000002-200-22000000
χ682-2-2-2222-22-22-22-2-222-2-22-2-222-2-222000000000000-222-20000000000000000-222-2-222-20000000000000000000000-22002-2000000
χ69444-44-4-4-4400004-44-44-4-40000000000004i−4i000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ70444-44-4-4-4400004-44-44-4-4000000000000−4i4i00000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ71444-44-4-4-4-20000-22-22-22223−2323−2323−2323−2300004i−4i0000000000−2i32i3−2i32i3−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-20000-22-22-22223−2323−2323−2323−230000−4i4i00000000002i3−2i32i3−2i32i−2i2i−2i00000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-20000-22-22-222−2323−2323−2323−232300004i−4i00000000002i3−2i32i3−2i3−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-20000-22-22-222−2323−2323−2323−23230000−4i4i0000000000−2i32i3−2i32i32i−2i2i−2i00000000000000000000000000000000000000000000000000
χ7544-44-44-4-4400004-4-44-44-40000000000000000−2i22i2−2i22i2000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ7644-44-44-4-4400004-4-44-44-400000000000000002i2−2i22i2−2i20000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ7744-44-44-4-4-20000-222-22-2223−23−2323−232323−2300000000−2i22i2−2i22i20000000000002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000
χ7844-44-44-4-4-20000-222-22-2223−23−2323−232323−23000000002i2−2i22i2−2i2000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000000000
χ7944-44-44-4-4-20000-222-22-22−232323−2323−23−232300000000−2i22i2−2i22i20000000000002ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000000000
χ8044-44-44-4-4-20000-222-22-22−232323−2323−23−2323000000002i2−2i22i2−2i2000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000000000
χ8144-4-4-4-4444-444-444-4-4-4-44-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ8244-4-4-4-444-24-4-44-2-22222-2-2-22222-2-200000000000044-4-40000000000000000-2-222-2-2220000000000000000000000000000000000
χ8344-4-4-4-444-24-4-44-2-22222-2-2-22222-2-2000000000000-4-444000000000000000022-2-222-2-20000000000000000000000000000000000
χ8444-4-4-4-444-2-444-4-2-22222-222-2-2-2-222000000000000000000000000000000002323−23−23−23−2323230000000000000000000000000000000000
χ8544-4-4-4-444-2-444-4-2-22222-222-2-2-2-22200000000000000000000000000000000−23−2323232323−23−230000000000000000000000000000000000
χ864-44-4-44-4440000-44-444-4-400000000004-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ874-44-4-44-4440000-44-444-4-40000000000-44000000000000-444-4000000000000000000000000000000000000000000000000000000
χ884-44-4-44-44-200002-22-2-22223−2323−23−2323−2323004-4000000000000-222-223−23−232300000000000000000000000000000000000000000000000000
χ894-44-4-44-44-200002-22-2-22223−2323−23−2323−232300-440000000000002-2-22−232323−2300000000000000000000000000000000000000000000000000
χ904-44-4-44-44-200002-22-2-222−2323−232323−2323−23004-4000000000000-222-2−232323−2300000000000000000000000000000000000000000000000000
χ914-44-4-44-44-200002-22-2-222−2323−232323−2323−2300-440000000000002-2-2223−23−232300000000000000000000000000000000000000000000000000
χ924-4-444-4-4440000-444-4-44-4000000000000000022−22−222200000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ934-4-444-4-4440000-444-4-44-40000000000000000−222222−22000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ944-4-444-4-44-200002-2-222-2223−23−232323−23−23230000000022−22−22220000000000002ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000000000
χ954-4-444-4-44-200002-2-222-2223−23−232323−23−232300000000−222222−22000000000000−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000000000
χ964-4-444-4-44-200002-2-222-22−232323−23−232323−230000000022−22−22220000000000002ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000000000000000
χ974-4-444-4-44-200002-2-222-22−232323−23−232323−2300000000−222222−22000000000000−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000000000000000
χ984-4-4-4444-444-44-4-4-444-4-4444-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-4-4444-4-24-44-422-2-222-2-2-222-2-2220000000000000000000000000000000023−23−2323−232323−230000000000000000000000000000000000
χ1004-4-4-4444-4-24-44-422-2-222-2-2-222-2-22200000000000000000000000000000000−232323−2323−23−23230000000000000000000000000000000000
χ1014-4-4-4444-4-2-44-4422-2-222-222-2-222-2-20000000000004-4-440000000000000000-222-2-222-20000000000000000000000000000000000
χ1024-4-4-4444-4-2-44-4422-2-222-222-2-222-2-2000000000000-444-400000000000000002-2-222-2-220000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.