Finite Group Databasebeta

← Group #10691024

Character table — Group #10691024

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222234444446661212121222444446666668888121212121212121212122424242424242424246688888812121212242424242424242424242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-111-1-1111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11111ii−i−i11-1-111-1-1-1-1iiii−i−i−i−i-11-1-1i−iii−i−i1-111ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11111ii−i−i11-1-111-1-1-1-1iiii−i−i−i−i-11-1-1i−iii−i−i1-111ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11111−i−iii11-1-111-1-1-1-1−i−i−i−iiiii-11-1-1−ii−i−iii1-111−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-11111−i−iii11-1-111-1-1-1-1−i−i−i−iiiii-11-1-1−ii−i−iii1-111−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i11-1-1111111iiii−i−i−i−i1-111i−i−i−iii1-1-1-1ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i11-1-1111111iiii−i−i−i−i1-111i−i−i−iii1-1-1-1ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1−i−iii11-1-1111111−i−i−i−iiiii1-111−iiii−i−i1-1-1-1−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-11-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1−i−iii11-1-1111111−i−i−i−iiiii1-111−iiii−i−i1-1-1-1−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222-2-2-2-2222-2-2-2-2002-200-22200000000-2-222-2-20000000000000000002i−2i2i−2i2-20000002i2i−2i−2i2i2i−2i−2i000000000000
χ18222222222-2-2-2-2222-2-2-2-2002-200-22200000000-2-222-2-2000000000000000000−2i2i−2i2i2-2000000−2i−2i2i2i−2i−2i2i2i000000000000
χ192222222-2-222-2-2222222200-2200-22200002222-2-2-2-2220000222222220000-2-20000-2-200-2-2-2-200000000000000000000
χ202222222-2-222-2-2222222200-2200-2220000-2-2-2-2-2-2-2-2220000-2-2-2-2-2-2-2-20000220000-2-200222200000000000000000000
χ212222222-2-2-2-222222-2-2-2-222-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000002-222000000-22-2-2000000000000000000000000
χ222222222-2-2-2-222222-2-2-2-2-2-2-2-222222-2-2-2-2000022-2-2-2-2222200000000-22-2-2000000-2222000000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111122-1-1-2-2-2-2-2-2-1-1-1-1111111111111000000000000
χ25222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-111112222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-21122-2-2-2-2-1-111-1-1-1-111111111000000000000
χ26222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-11111-2-2-2-2-1-1-1-1-1-1111111111111-2-211-2-22222-1-1111111-1-1-1-1-1-1-1-1000000000000
χ27222222-122-2-2-2-2-1-1-11111002-200-2-1-1−i3−i3i3i3000011-1-111−i3−i3i3i333−3−333−3−300−i3i3002i−2i2i−2i-11−i3i33−33−3−i−iii−i−iii000000000000
χ28222222-122-2-2-2-2-1-1-11111002-200-2-1-1−i3−i3i3i3000011-1-111−i3−i3i3i3−3−333−3−33300−i3i300−2i2i−2i2i-11−i3i3−33−33ii−i−iii−i−i000000000000
χ29222222-122-2-2-2-2-1-1-11111002-200-2-1-1i3i3−i3−i3000011-1-111i3i3−i3−i333−3−333−3−300i3−i300−2i2i−2i2i-11i3−i33−33−3ii−i−iii−i−i000000000000
χ30222222-122-2-2-2-2-1-1-11111002-200-2-1-1i3i3−i3−i3000011-1-111i3i3−i3−i3−3−333−3−33300i3−i3002i−2i2i−2i-11i3−i3−33−33−i−iii−i−iii000000000000
χ31222222-1-2-222-2-2-1-1-1-1-1-1-100-2200-2-1-1−i3−i3i3i322221111-1-1i3i3−i3−i3-1-1-1-1-1-1-1-100−i3i3-2-2000011i3−i31111−i3i3−i3i3−i3i3−i3i3000000000000
χ32222222-1-2-222-2-2-1-1-1-1-1-1-100-2200-2-1-1−i3−i3i3i3-2-2-2-21111-1-1i3i3−i3−i31111111100−i3i322000011i3−i3-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000
χ33222222-1-2-222-2-2-1-1-1-1-1-1-100-2200-2-1-1i3i3−i3−i322221111-1-1−i3−i3i3i3-1-1-1-1-1-1-1-100i3−i3-2-2000011−i3i31111i3−i3i3−i3i3−i3i3−i3000000000000
χ34222222-1-2-222-2-2-1-1-1-1-1-1-100-2200-2-1-1i3i3−i3−i3-2-2-2-21111-1-1−i3−i3i3i31111111100i3−i322000011−i3i3-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000
χ35222222-1-2-2-2-222-1-1-1111122-2-2-2-22-1-1-1-1-1-10000-1-11111111133−3−333−3−32-2-1-10000001-111−33−333−3−333−3−33000000000000
χ36222222-1-2-2-2-222-1-1-1111122-2-2-2-22-1-1-1-1-1-10000-1-111111111−3−333−3−3332-2-1-10000001-1113−33−3−333−3−333−3000000000000
χ37222222-1-2-2-2-222-1-1-11111-2-2-2-2222-1-111110000-1-11111-1-1-1-133−3−333−3−3-22110000001-1-1-1−33−33−333−3−333−3000000000000
χ38222222-1-2-2-2-222-1-1-11111-2-2-2-2222-1-111110000-1-11111-1-1-1-1−3−333−3−333-22110000001-1-1-13−33−33−3−333−3−33000000000000
χ392222-2-22222222222222222-2-222-2-2-2222200002222-2-2222200000000-2-2-2-2000000-2-2-2-2000000000000000000000000
χ402222-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2000000002222000000-2-222000000000000000000000000
χ412222-2-2222-2-2-2-2222-2-2-2-200-22002-2-200002i2i−2i−2i-2-2222200002i2i2i2i−2i−2i−2i−2i0000−2i2i0000-2200−2i−2i2i2i00000000000000000000
χ422222-2-2222-2-2-2-2222-2-2-2-200-22002-2-20000−2i−2i2i2i-2-222220000−2i−2i−2i−2i2i2i2i2i00002i−2i0000-22002i2i−2i−2i00000000000000000000
χ432222-2-22-2-222-2-22222222002-2002-2-200000000-2-2-2-2-2-20000000000000000002-2-222200000022-2-2-2-222000000000000
χ442222-2-22-2-222-2-22222222002-2002-2-200000000-2-2-2-2-2-2000000000000000000-222-222000000-2-22222-2-2000000000000
χ452222-2-2-1222222-1-1-1-1-1-1-122-2-222-211-1-1-1-10000-1-1-1-111-1-1-1-1−i3−i3i3i3i3i3−i3−i3-2-2110000001111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ462222-2-2-1222222-1-1-1-1-1-1-122-2-222-211-1-1-1-10000-1-1-1-111-1-1-1-1i3i3−i3−i3−i3−i3i3i3-2-2110000001111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
χ472222-2-2-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-21111110000-1-1-1-1111111−i3−i3i3i3i3i3−i3−i322-1-100000011-1-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ482222-2-2-1222222-1-1-1-1-1-1-1-2-2-2-2-2-2-21111110000-1-1-1-1111111i3i3−i3−i3−i3−i3i3i322-1-100000011-1-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ492222-2-2-122-2-2-2-2-1-1-1111100-2200211−i3−i3i3i32i2i−2i−2i11-1-1-1-1−i3−i3i3i3−i−i−i−iiiii00i3−i3−2i2i00001-1i3−i3ii−i−i3−33−3−33−33000000000000
χ502222-2-2-122-2-2-2-2-1-1-1111100-2200211−i3−i3i3i3−2i−2i2i2i11-1-1-1-1−i3−i3i3i3iiii−i−i−i−i00i3−i32i−2i00001-1i3−i3−i−iii−33−333−33−3000000000000
χ512222-2-2-122-2-2-2-2-1-1-1111100-2200211i3i3−i3−i32i2i−2i−2i11-1-1-1-1i3i3−i3−i3−i−i−i−iiiii00−i3i3−2i2i00001-1−i3i3ii−i−i−33−333−33−3000000000000
χ522222-2-2-122-2-2-2-2-1-1-1111100-2200211i3i3−i3−i3−2i−2i2i2i11-1-1-1-1i3i3−i3−i3iiii−i−i−i−i00−i3i32i−2i00001-1−i3i3−i−iii3−33−3−33−33000000000000
χ532222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211−i3−i3i3i30000111111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300i3−i3002-2-22-1-1−i3i3−i3i3i3−i3-1-11111-1-1000000000000
χ542222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211−i3−i3i3i30000111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300i3−i300-222-2-1-1−i3i3i3−i3−i3i311-1-1-1-111000000000000
χ552222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211i3i3−i3−i30000111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300−i3i300-222-2-1-1i3−i3−i3i3i3−i311-1-1-1-111000000000000
χ562222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211i3i3−i3−i30000111111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300−i3i3002-2-22-1-1i3−i3i3−i3−i3i3-1-11111-1-1000000000000
χ572222-2-2-1-2-2-2-222-1-1-111112222-2-2-211-1-1-1-12i2i−2i−2i-1-111-1-11111−i−i−i−iiiii-22112i−2i2i2i−2i−2i-11-1-1−i−iii−i−i−i−iiiii000000000000
χ582222-2-2-1-2-2-2-222-1-1-111112222-2-2-211-1-1-1-1−2i−2i2i2i-1-111-1-11111iiii−i−i−i−i-2211−2i2i−2i−2i2i2i-11-1-1ii−i−iiiii−i−i−i−i000000000000
χ592222-2-2-1-2-2-2-222-1-1-11111-2-22222-21111112i2i−2i−2i-1-111-1-1-1-1-1-1−i−i−i−iiiii2-2-1-12i−2i−2i−2i2i2i-1111−i−iiiiiii−i−i−i−i000000000000
χ602222-2-2-1-2-2-2-222-1-1-11111-2-22222-2111111−2i−2i2i2i-1-111-1-1-1-1-1-1iiii−i−i−i−i2-2-1-1−2i2i2i2i−2i−2i-1111ii−i−i−i−i−i−iiiii000000000000
χ612-22-20022i−2i2i−2i2-22-2-22i2i−2i−2i2-2002i−2i0002-22-200002-22i−2i002i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ622-22-20022i−2i2i−2i2-22-2-22i2i−2i−2i2-2002i−2i0002-22-200002-22i−2i002i−2i2i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ632-22-20022i−2i2i−2i2-22-2-22i2i−2i−2i-2200−2i2i000-22-2200002-22i−2i00−2i2i−2i2i00000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ642-22-20022i−2i2i−2i2-22-2-22i2i−2i−2i-2200−2i2i000-22-2200002-22i−2i00−2i2i−2i2i0000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ652-22-2002−2i2i−2i2i2-22-2-2−2i−2i2i2i2-200−2i2i0002-22-200002-2−2i2i00−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-2002−2i2i−2i2i2-22-2-2−2i−2i2i2i2-200−2i2i0002-22-200002-2−2i2i00−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ672-22-2002−2i2i−2i2i2-22-2-2−2i−2i2i2i-22002i−2i000-22-2200002-2−2i2i002i−2i2i−2i00000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ682-22-2002−2i2i−2i2i2-22-2-2−2i−2i2i2i-22002i−2i000-22-2200002-2−2i2i002i−2i2i−2i0000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ6944-4-44-44000000-44-4000000000004-4000022−2222−22000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ7044-4-44-44000000-44-4000000000004-40000−2222−22220000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ7144-4-44-4-20000002-2223−2323−230000000-22000022−2222−22000023−2300002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000
χ7244-4-44-4-20000002-2223−2323−230000000-220000−2222−2222000023−230000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000
χ7344-4-44-4-20000002-22−2323−23230000000-22000022−2222−220000−232300002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000
χ7444-4-44-4-20000002-22−2323−23230000000-220000−2222−22220000−23230000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000
χ7544-4-4-444000000-44-400000000000-440000−2i22i22i2−2i20000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ7644-4-4-444000000-44-400000000000-4400002i2−2i2−2i22i200000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ7744-4-4-44-20000002-2223−2323−2300000002-20000−2i22i22i2−2i20000−232300002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ7844-4-4-44-20000002-2223−2323−2300000002-200002i2−2i2−2i22i20000−23230000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000
χ7944-4-4-44-20000002-22−2323−232300000002-20000−2i22i22i2−2i2000023−2300002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ8044-4-4-44-20000002-22−2323−232300000002-200002i2−2i2−2i22i2000023−230000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ814-44-40044i−4i−4i4i-444-4-4−4i−4i4i4i00000000000000000-444i−4i0000000000000000000000000000000000000000000000000000
χ824-44-4004−4i4i4i−4i-444-4-44i4i−4i−4i00000000000000000-44−4i4i0000000000000000000000000000000000000000000000000000
χ834-44-400-24i−4i4i−4i4-4-222−2i−2i2i2i4-4004i−4i000-22-220000-22−2i2i00−2i2i−2i2i0000000000000000000000000000000000000000000000
χ844-44-400-24i−4i4i−4i4-4-222−2i−2i2i2i-4400−4i4i0002-22-20000-22−2i2i002i−2i2i−2i0000000000000000000000000000000000000000000000
χ854-44-400-24i−4i−4i4i-44-2222i2i−2i−2i000000000−2i32i32i3−2i300002-2−2i2i0023−23−23230000000000000000000000000000000000000000000000
χ864-44-400-24i−4i−4i4i-44-2222i2i−2i−2i0000000002i3−2i3−2i32i300002-2−2i2i00−232323−230000000000000000000000000000000000000000000000
χ874-44-400-2−4i4i4i−4i-44-222−2i−2i2i2i000000000−2i32i32i3−2i300002-22i−2i00−232323−230000000000000000000000000000000000000000000000
χ884-44-400-2−4i4i4i−4i-44-222−2i−2i2i2i0000000002i3−2i3−2i32i300002-22i−2i0023−23−23230000000000000000000000000000000000000000000000
χ894-44-400-2−4i4i−4i4i4-4-2222i2i−2i−2i4-400−4i4i000-22-220000-222i−2i002i−2i2i−2i0000000000000000000000000000000000000000000000
χ904-44-400-2−4i4i−4i4i4-4-2222i2i−2i−2i-44004i−4i0002-22-20000-222i−2i00−2i2i−2i2i0000000000000000000000000000000000000000000000
χ918-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-400000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-400000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000000000

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