Finite Group Databasebeta

← Group #10690074

Character table — Group #10690074

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222444422344444466612121212224444666666888812121212121212121212242424242424242444888888121212121212242424242424242424242424888888888888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-11111ii−i−i1111-1-1-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-11111ii−i−i1111-1-1-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-11111−i−iii1111-1-1-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1-11111−i−iii1111-1-1-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1ii−i−i1111-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1ii−i−i1111-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1−i−iii1111-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1−i−iii1111-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ1722222222222-2-22-2-22222222222-222-2222222000022-2-2-2-2222200000000-2-2000000-2-2-2-2-2-2000000000000000000000000000000
χ1822222222222-2-22-2-222222222-2-2-2-2-2-222-2-2-2-2000022-2-2-2-2-2-2-2-20000000022000000-2-22222000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ202222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ212222222222-1222222-1-1-1-1-1-1-1-2-22-2-22-1-111112222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000000000
χ222222222222-1222222-1-1-1-1-1-1-1-2-22-2-22-1-11111-2-2-2-2-1-1-1-1-1-1111111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000000000
χ232222222222-1-2-22-2-22-1-1-1-1-1-1-122-222-2-1-1-1-1-1-10000-1-11111-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2000000111111−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ242222222222-1-2-22-2-22-1-1-1-1-1-1-122-222-2-1-1-1-1-1-10000-1-11111-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2000000111111i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ252222222222-1-2-22-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111110000-1-111111111−i3−i3i3i3−i3−i3i3i32200000011-1-1-1-1−i3i3−i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ262222222222-1-2-22-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2-1-111110000-1-111111111i3i3−i3−i3i3i3−i3−i32200000011-1-1-1-1i3−i3i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ2722222222-2-2222-222-2222222200-200-2-2-200002222-2-2222200002222222200-2-20000-2-20000-2-2-2-200000000000000000000000000
χ2822222222-2-2222-222-2222222200-200-2-2-20000-2-2-2-2-2-222220000-2-2-2-2-2-2-2-200220000-2-20000222200000000000000000000000000
χ2922222222-2-22-2-2-2-2-2-22222222002002-2-200000000-2-2-2-2-2-200000000000000002-22-222000000002-22-22-22-2000000000000000000
χ3022222222-2-22-2-2-2-2-2-22222222002002-2-200000000-2-2-2-2-2-20000000000000000-22-222200000000-22-22-22-22000000000000000000
χ3122222222-2-2-122-222-2-1-1-1-1-1-1-100-200-211−i3−i3i3i3222211-1-1-1-1−i3−i3i3i3-1-1-1-1-1-1-1-100-2-2000011−i3i3−i3i31111−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3222222222-2-2-122-222-2-1-1-1-1-1-1-100-200-211−i3−i3i3i3-2-2-2-211-1-1-1-1−i3−i3i3i3111111110022000011−i3i3−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3322222222-2-2-122-222-2-1-1-1-1-1-1-100-200-211i3i3−i3−i3222211-1-1-1-1i3i3−i3−i3-1-1-1-1-1-1-1-100-2-2000011i3−i3i3−i31111i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3422222222-2-2-122-222-2-1-1-1-1-1-1-100-200-211i3i3−i3−i3-2-2-2-211-1-1-1-1i3i3−i3−i3111111110022000011i3−i3i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3522222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-100200211−i3−i3i3i30000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300002-22-2-1-1i3−i3i3−i3i3−i3i3−i3-11-11-11-11000000000000000000
χ3622222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-100200211−i3−i3i3i30000111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000-22-22-1-1i3−i3i3−i3−i3i3−i3i31-11-11-11-1000000000000000000
χ3722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-100200211i3i3−i3−i30000111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000-22-22-1-1−i3i3−i3i3i3−i3i3−i31-11-11-11-1000000000000000000
χ3822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-100200211i3i3−i3−i30000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300002-22-2-1-1−i3i3−i3i3−i3i3−i3i3-11-11-11-11000000000000000000
χ392222-2-2-2-222222-2-2-2-2222-2-2-2-200-20022200002i2i−2i−2i-2-222-2-200002i2i2i2i−2i−2i−2i−2i00−2i2i0000-220000−2i−2i2i2i00000000000000000000000000
χ402222-2-2-2-222222-2-2-2-2222-2-2-2-200-2002220000−2i−2i2i2i-2-222-2-20000−2i−2i−2i−2i2i2i2i2i002i−2i0000-2200002i2i−2i−2i00000000000000000000000000
χ412222-2-2-2-2222-2-2-222-2222-2-2-2-200200-22200000000-2-2-2-22200000000000000002i−2i−2i2i2-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ422222-2-2-2-2222-2-2-222-2222-2-2-2-200200-22200000000-2-2-2-2220000000000000000−2i2i2i−2i2-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ432222-2-2-2-222-122-2-2-2-2-1-1-1111100-2002-1-1−i3−i3i3i32i2i−2i−2i11-1-111i3i3−i3−i3−i−i−i−iiiii00−2i2i00001-1−i3i3i3−i3ii−i−i3−3−33−333−3000000000000000000
χ442222-2-2-2-222-122-2-2-2-2-1-1-1111100-2002-1-1−i3−i3i3i3−2i−2i2i2i11-1-111i3i3−i3−i3iiii−i−i−i−i002i−2i00001-1−i3i3i3−i3−i−iii−333−33−3−33000000000000000000
χ452222-2-2-2-222-122-2-2-2-2-1-1-1111100-2002-1-1i3i3−i3−i32i2i−2i−2i11-1-111−i3−i3i3i3−i−i−i−iiiii00−2i2i00001-1i3−i3−i3i3ii−i−i−333−33−3−33000000000000000000
χ462222-2-2-2-222-122-2-2-2-2-1-1-1111100-2002-1-1i3i3−i3−i3−2i−2i2i2i11-1-111−i3−i3i3i3iiii−i−i−i−i002i−2i00001-1i3−i3−i3i3−i−iii3−3−33−333−3000000000000000000
χ472222-2-2-2-222-1-2-2-222-2-1-1-1111100200-2-1-1−i3−i3i3i300001111-1-1i3i3−i3−i333−3−3−3−33300002i−2i−2i2i-11i3−i3−i3i3−333−3−ii−iii−ii−i000000000000000000
χ482222-2-2-2-222-1-2-2-222-2-1-1-1111100200-2-1-1−i3−i3i3i300001111-1-1i3i3−i3−i3−3−33333−3−30000−2i2i2i−2i-11i3−i3−i3i33−3−33i−ii−i−ii−ii000000000000000000
χ492222-2-2-2-222-1-2-2-222-2-1-1-1111100200-2-1-1i3i3−i3−i300001111-1-1−i3−i3i3i333−3−3−3−3330000−2i2i2i−2i-11−i3i3i3−i3−333−3i−ii−i−ii−ii000000000000000000
χ502222-2-2-2-222-1-2-2-222-2-1-1-1111100200-2-1-1i3i3−i3−i300001111-1-1−i3−i3i3i3−3−33333−3−300002i−2i−2i2i-11−i3i3i3−i33−3−33−ii−iii−ii−i000000000000000000
χ512222-2-2-2-2-2-22-2-22222222-2-2-2-222-2-2-22-2-22222000022-2-222-2-2-2-200000000-22000000-22-2-222000000000000000000000000000000
χ522222-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2222-2-2-2-2-2-2000022-2-2222222000000002-2000000-2222-2-2000000000000000000000000000000
χ532222-2-2-2-2-2-2-1222-2-22-1-1-11111222-2-2-211-1-1-1-12i2i−2i−2i-1-1-1-1111111−i−i−i−iiiii2-22i−2i2i2i−2i−2i-11-1-111−i−iii−i−i−i−iiiii000000000000000000
χ542222-2-2-2-2-2-2-1222-2-22-1-1-11111222-2-2-211-1-1-1-1−2i−2i2i2i-1-1-1-1111111iiii−i−i−i−i2-2−2i2i−2i−2i2i2i-11-1-111ii−i−iiiii−i−i−i−i000000000000000000
χ552222-2-2-2-2-2-2-1222-2-22-1-1-11111-2-2222-21111112i2i−2i−2i-1-1-1-111-1-1-1-1−i−i−i−iiiii-222i−2i−2i−2i2i2i-1111-1-1−i−iiiiiii−i−i−i−i000000000000000000
χ562222-2-2-2-2-2-2-1222-2-22-1-1-11111-2-2222-2111111−2i−2i2i2i-1-1-1-111-1-1-1-1iiii−i−i−i−i-22−2i2i2i2i−2i−2i-1111-1-1ii−i−i−i−i−i−iiiii000000000000000000
χ572222-2-2-2-2-2-2-1-2-22222-1-1-1111122-2-2-2211-1-1-1-10000-1-111-1-1111133−3−3−3−333-220000001-111-1-13−3−3333−3−3−3−333000000000000000000
χ582222-2-2-2-2-2-2-1-2-22222-1-1-1111122-2-2-2211-1-1-1-10000-1-111-1-11111−3−33333−3−3-220000001-111-1-1−333−3−3−33333−3−3000000000000000000
χ592222-2-2-2-2-2-2-1-2-22222-1-1-11111-2-2-22221111110000-1-111-1-1-1-1-1-133−3−3−3−3332-20000001-1-1-1113−3−33−3−33333−3−3000000000000000000
χ602222-2-2-2-2-2-2-1-2-22222-1-1-11111-2-2-22221111110000-1-111-1-1-1-1-1-1−3−33333−3−32-20000001-1-1-111−333−333−3−3−3−333000000000000000000
χ6122-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002−2−i2i200
χ6222-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−22i2−i200
χ6322-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−22i2−i200
χ6422-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002−2−i2i200
χ6522-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00002−2i2−i200
χ6622-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−22−i2i200
χ6722-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−22−i2i200
χ6822-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002−2i2−i200
χ692-2-2222-2-22-2200-2002-22-222-2-22-202-202-22-22-200002-200002-22-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ702-2-2222-2-22-2200-2002-22-222-2-22-202-202-22-22-200002-200002-22-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ712-2-2222-2-22-2200-2002-22-222-2-2-220-2202-2-22-2200002-20000-22-220000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ722-2-2222-2-22-2200-2002-22-222-2-2-220-2202-2-22-2200002-20000-22-220000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ732-2-22-2-222-22200-2002-22-2-2-2222-20-220-222-22-200002-20000-22-2200000000000000000000000000000000002−22−2−22−222−2−22000000
χ742-2-22-2-222-22200-2002-22-2-2-2222-20-220-222-22-200002-20000-22-220000000000000000000000000000000000−22−222−22−2−222−2000000
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χ7844-4-44i−4i4i−4i00-24-404i−4i0-222−2i2i−2i2i0000000000004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300-22−2i2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000000000000000
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χ944-4-4444-4-4-44-200400-42-22-2-2220000002-2−2i32i32i3−2i300002-20000−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ954-4-4444-4-4-44-200400-42-22-2-2220000002-22i3−2i3−2i32i300002-200002i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
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χ1004-4-44-4-444-44-200-40042-2222-2-2-4404-402-22-22-20000-220000-22-220000000000000000000000000000000000000000000000000000
χ1018-88-88i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000

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