Finite Group Databasebeta

← Group #10691864

Character table — Group #10691864

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12222234444666121212124444668888121212121212121212128888888888242424242424242424242424242424242424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111-1-111111111-11-1-1-1ii−i−i11-1-111-1-1-1-1i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1111-1-111111111-11-1-1-1ii−i−i11-1-111-1-1-1-1i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1111-1-111111111-11-1-1-1ii−i−i11-1-111-1-1-1-1i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1111-1-111111111-11-1-1-1ii−i−i11-1-111-1-1-1-1i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1111-1-111111111-11-1-1-1−i−iii11-1-111-1-1-1-1−ii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1111-1-111111111-11-1-1-1−i−iii11-1-111-1-1-1-1−ii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1111-1-111111111-11-1-1-1−i−iii11-1-111-1-1-1-1−ii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1111-1-111111111-11-1-1-1−i−iii11-1-111-1-1-1-1−ii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-22200000000-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-22200002222-2-2-2-2-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ202222222-2-2-2-2222-2-2-2-222-2-22200002222-2-2-2-2-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ212222222-2-2-2-2222-2-2-2-2-2-222220000-2-2-2-222-2-22200000000000000000000000000000000002-22-200000000
χ222222222-2-2-2-2222-2-2-2-2-2-222220000-2-2-2-222-2-2220000000000000000000000000000000000-22-2200000000
χ23222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222111111-1-111-2-200000000-1-111-1-11133−3−333−3−333−3−333−3−3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222111111-1-111-2-200000000-1-111-1-111−3−333−3−333−3−333−3−333000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2111111-1-111220000000011-1-111-1-133−3−333−3−3−3−333−3−333000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2111111-1-111220000000011-1-111-1-1−3−333−3−33333−3−333−3−3000000000000
χ312222-2-2222-2-22222222-22-22-2-22i2i−2i−2i-2-222-2-2-2-222−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2222-2-22222222-22-22-2-2−2i−2i2i2i-2-222-2-2-2-2222i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-22-2-222222-2-2-2-22-2-22-2-2000022-2-2-2-22222000000000000000000000000000000000000002-2-220000
χ342222-2-22-2-222222-2-2-2-22-2-22-2-2000022-2-2-2-2222200000000000000000000000000000000000000-222-20000
χ352222-2-22-2-222222-2-2-2-2-222-2-2-20000-2-2222222-2-200000000000000000000000000000000002-2-2200000000
χ362222-2-22-2-222222-2-2-2-2-222-2-2-20000-2-2222222-2-20000000000000000000000000000000000-222-200000000
χ372222-2-2-122-2-2-1-1-1-1-1-1-12-22-2112i2i−2i−2i-1-111-1-111112i−2i22-2-22i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii000000000000
χ382222-2-2-122-2-2-1-1-1-1-1-1-12-22-2112i2i−2i−2i-1-111-1-111112i−2i-2-222−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i000000000000
χ392222-2-2-122-2-2-1-1-1-1-1-1-12-22-211−2i−2i2i2i-1-111-1-11111−2i2i22-2-2−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i000000000000
χ402222-2-2-122-2-2-1-1-1-1-1-1-12-22-211−2i−2i2i2i-1-111-1-11111−2i2i-2-2222i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii000000000000
χ412222-2-2-122-2-2-1-1-1-1-1-1-1-22-22112i2i−2i−2i11-1-11111-1-1−2i2i00000000−i−iiiii−i−i33−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ422222-2-2-122-2-2-1-1-1-1-1-1-1-22-22112i2i−2i−2i11-1-11111-1-1−2i2i00000000−i−iiiii−i−i−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ432222-2-2-122-2-2-1-1-1-1-1-1-1-22-2211−2i−2i2i2i11-1-11111-1-12i−2i00000000ii−i−i−i−iii33−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ442222-2-2-122-2-2-1-1-1-1-1-1-1-22-2211−2i−2i2i2i11-1-11111-1-12i−2i00000000ii−i−i−i−iii−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ452-2-222-222-2-222-2-222-2-200002-22i−2i2i−2i0000002-20000−i2i2−i2i22−22−22i−2i002i−2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ462-2-222-222-2-222-2-222-2-200002-22i−2i2i−2i0000002-20000i2−i2i2−i2−22−222i−2i002i−2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ472-2-222-222-2-222-2-222-2-200002-2−2i2i−2i2i0000002-20000−i2i2−i2i2−22−22−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ482-2-222-222-2-222-2-222-2-200002-2−2i2i−2i2i0000002-20000i2−i2i2−i22−22−2−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ492-2-222-2-12-2-22-111-1-1110000-112i−2i2i−2i3−33−33−3-113−300−i2i2−i2i22−22−2−ii−i3i3−ii−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ502-2-222-2-12-2-22-111-1-1110000-112i−2i2i−2i3−33−33−3-113−300i2−i2i2−i2−22−22−ii−i3i3−ii−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ512-2-222-2-12-2-22-111-1-1110000-112i−2i2i−2i−33−33−33-11−3300−i2i2−i2i22−22−2−iii3−i3−iii3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ522-2-222-2-12-2-22-111-1-1110000-112i−2i2i−2i−33−33−33-11−3300i2−i2i2−i2−22−22−iii3−i3−iii3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ532-2-222-2-12-2-22-111-1-1110000-11−2i2i−2i2i3−33−33−3-113−300−i2i2−i2i2−22−22i−ii3−i3i−ii3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ542-2-222-2-12-2-22-111-1-1110000-11−2i2i−2i2i3−33−33−3-113−300i2−i2i2−i22−22−2i−ii3−i3i−ii3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ552-2-222-2-12-2-22-111-1-1110000-11−2i2i−2i2i−33−33−33-11−3300−i2i2−i2i2−22−22i−i−i3i3i−i−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ562-2-222-2-12-2-22-111-1-1110000-11−2i2i−2i2i−33−33−33-11−3300i2−i2i2−i22−22−2i−i−i3i3i−i−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ572-2-22-2222-22-22-2-222-2-20000-222-2-22000000-220000−i2i2i2−i2−i2i2i2−i22-200-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ582-2-22-2222-22-22-2-222-2-20000-222-2-22000000-220000i2−i2−i2i2i2−i2−i2i22-200-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ592-2-22-2222-22-22-2-222-2-20000-22-222-2000000-220000−i2i2i2−i2i2−i2−i2i2-22002-200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ602-2-22-2222-22-22-2-222-2-20000-22-222-2000000-220000i2−i2−i2i2−i2i2i2−i2-22002-200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ612-2-22-22-12-22-2-111-1-11100001-12-2-223−3−333−31-1−3300−i2i2i2−i2−i2i2i2−i2-11−331-13−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ622-2-22-22-12-22-2-111-1-11100001-12-2-223−3−333−31-1−3300i2−i2−i2i2i2−i2−i2i2-11−331-13−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ632-2-22-22-12-22-2-111-1-11100001-12-2-22−333−3−331-13−300−i2i2i2−i2−i2i2i2−i2-113−31-1−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ642-2-22-22-12-22-2-111-1-11100001-12-2-22−333−3−331-13−300i2−i2−i2i2i2−i2−i2i2-113−31-1−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ652-2-22-22-12-22-2-111-1-11100001-1-222-23−3−333−31-1−3300−i2i2i2−i2i2−i2−i2i21-13−3-11−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ662-2-22-22-12-22-2-111-1-11100001-1-222-23−3−333−31-1−3300i2−i2−i2i2−i2i2i2−i21-13−3-11−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ672-2-22-22-12-22-2-111-1-11100001-1-222-2−333−3−331-13−300−i2i2i2−i2i2−i2−i2i21-1−33-113−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ682-2-22-22-12-22-2-111-1-11100001-1-222-2−333−3−331-13−300i2−i2−i2i2−i2i2i2−i21-1−33-113−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ69444444-2-4-4-4-4-2-2-2222244-4-4-2-20000-2-2-2-22222220000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-22222-4-444-2-200002222-2-222-2-20000000000000000000000000000000000000000000000
χ714444-4-4-2-4-444-2-2-222224-4-44220000-2-22222-2-2-2-20000000000000000000000000000000000000000000000
χ724444-4-4-2-4-444-2-2-22222-444-422000022-2-2-2-2-2-2220000000000000000000000000000000000000000000000
χ734-4-444-44-444-44-4-4-4-44400004-40000000000-44000000000000000000000000000000000000000000000000
χ744-4-444-4-2-444-4-22222-2-20000-22000023−2323−23−23232-2−23230000000000000000000000000000000000000000000000
χ754-4-444-4-2-444-4-22222-2-20000-220000−2323−232323−232-223−230000000000000000000000000000000000000000000000
χ764-4-44-444-44-444-4-4-4-4440000-4400000000004-4000000000000000000000000000000000000000000000000
χ774-4-44-44-2-44-44-22222-2-200002-2000023−23−2323−2323-2223−230000000000000000000000000000000000000000000000
χ784-4-44-44-2-44-44-22222-2-200002-20000−232323−2323−23-22−23230000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000000

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